Introduction to Parametric Equations

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Questions

• How do you find the parametric equation of a parabola?
• How do you find the parametric equations for a line segment?
• How do you find the parametric equations for a line through a point?
• How do you find the parametric equations for the rectangular equation #x^2+y^2-25=0# ?
• How do you find the parametric equations of a circle?
• How do you find the parametric equations of a curve?
• What are parametric equations used for?
• What is the parametric equation of an ellipse?
• How do you sketch the curve with parametric equations #x = sin(t)#, #y=sin^2(t)# ?
• How do you find the vector parametrization of the line of intersection of two planes #2x - y - z = 5# and #x - y + 3z = 2#?
• How do you use cos(t) and sin(t), with positive coefficients, to parametrize the intersection of the surfaces #x^2+y^2=25# and #z=3x^2#?
• How do you write #x = e^t-1# and #y=e^2t# as a cartesian equation and then sketch the curve?
• How do you graph parametric equations?
• For #f(t)= (t^2,t^3)# what is the distance between #f(1)# and #f(3)#?
• For #f(t)= (t^2,t^3)# what is the distance between #f(1)# and #f(3)#?
• For #f(t)= (t-t^3,t^3)# what is the distance between #f(0)# and #f(3)#?
• For #f(t)= ( t-2, sqrtt -t )# what is the distance between #f(0)# and #f(1)#?
• For #f(t)= (t/(t+3), t/sqrt(t+1) -t )# what is the distance between #f(0)# and #f(1)#?
• For #f(t)= (t/(t-3), t/sqrt(t^2+1) )# what is the distance between #f(0)# and #f(1)#?
• For #f(t)= (1/(2t-3), t/sqrt(t^2+1) )# what is the distance between #f(0)# and #f(1)#?
• For #f(t)= (1/(2t-3), te^t )# what is the distance between #f(0)# and #f(1)#?
• For #f(t)= (e^(t^3-t^2), te^t )# what is the distance between #f(0)# and #f(1)#?
• For #f(t)= (lnt/e^t, e^t/t )# what is the distance between #f(1)# and #f(2)#?
• For #f(t)= (lnt/e^t, te^t)# what is the distance between #f(1)# and #f(2)#?
• For #f(t)= (lnt-e^t, t^2e^t)# what is the distance between #f(1)# and #f(2)#?
• For #f(t)= (lnt-e^t, t^2/e^t)# what is the distance between #f(2)# and #f(4)#?
• For #f(t)= (lnt/t, t^2/e^t)# what is the distance between #f(2)# and #f(4)#?
• For #f(t)= ((lnt)^2/t,t^3)# what is the distance between #f(2)# and #f(4)#?
• For #f(t)= (te^(3t),t^2-t)# what is the distance between #f(2)# and #f(5)#?
• For #f(t)= (te^(1-3t),2t^2-t)# what is the distance between #f(2)# and #f(5)#?
• For #f(t)= (t/e^(1-3t),2t^2-t)# what is the distance between #f(2)# and #f(5)#?
• For #f(t)= (e^t/t,4t+1/t)# what is the distance between #f(2)# and #f(5)#?
• For #f(t)= (1/t,-1/t^2)# what is the distance between #f(2)# and #f(5)#?
• For #f(t)= (1/(1-t),-1/(1+t^2))# what is the distance between #f(2)# and #f(5)#?
• For #f(t)= (sint-cost,t^2)# what is the distance between #f(2)# and #f(5)#?
• For #f(t)= (sint-cost,t)# what is the distance between #f(pi/4)# and #f(pi)#?
• For #f(t)= (sin^2t,t/pi-2)# what is the distance between #f(pi/4)# and #f(pi)#?
• For #f(t)= (sin^2t,cos^2t)# what is the distance between #f(pi/4)# and #f(pi)#?
• For #f(t)= (sint,cost)# what is the distance between #f(pi/4)# and #f(pi)#?
• For #f(t)= (sint,cos^2t/t)# what is the distance between #f(pi/4)# and #f(pi)#?
• For #f(t)= (sin2t,cos^2t)# what is the distance between #f(pi/4)# and #f(pi)#?
• For #f(t)= (cos2t,sin^2t)# what is the distance between #f(pi/4)# and #f(pi)#?
• For #f(t)= (cost/2,sin^2t)# what is the distance between #f(pi/4)# and #f(pi)#?
• For #f(t)= (sqrt(t+2)/(t+1),t^2+3t)# what is the distance between #f(0)# and #f(2)#?
• For #f(t)= (sqrt(t)/(t+1),t^2-t)# what is the distance between #f(0)# and #f(2)#?
• For #f(t)= (t/sqrt(t+1),t^2-t)# what is the distance between #f(0)# and #f(2)#?
• For #f(t)= (te^(t-1),t^2-t+1)# what is the distance between #f(0)# and #f(2)#?
• For #f(t)= (1/(t-3),t^2)# what is the distance between #f(0)# and #f(2)#?
• For #f(t)= (t^3-t^2+1,t^2-t)# what is the distance between #f(2)# and #f(5)#?
• For #f(t)= (t^3-t+1,t^2-t)# what is the distance between #f(2)# and #f(5)#?
• For #f(t)= (t/(t+2)-t+1,t^2-t)# what is the distance between #f(2)# and #f(5)#?
• For #f(t)= (t+21,-3t^2-2t)# what is the distance between #f(2)# and #f(5)#?
• For #f(t)= (t-2,-t^2-2t)# what is the distance between #f(2)# and #f(5)#?
• For #f(t)= ((t-1)^2,-t^2-2t)# what is the distance between #f(2)# and #f(5)#?
• For #f(t)= ((t+3)^2,t^3-t)# what is the distance between #f(2)# and #f(4)#?
• How do you find the parametric equations for the line through the point P = (3, 5, -2) that is perpendicular to the plane −5x + 1y + 3z = 1?
• How do write parametric equations for Margot's position t seconds after s if Margot is walking in a straight line from a point 30 feet due east of a statue from a point 24 feet due north of the statue and walks at a constant speed of four feet per second?
• How do you graph the curve whose parametric equations are given and show its orientation given #x = sqrt{t} + 4#, #y = sqrt{t} - 4#, where #t>=0#?
• How do you find the set of parametric equations for the line in 3D described by the general equations x-y-z=-4 and x+y-5z=-12?
• How do you find a vector equation for the line through the point (5, 1, 4) and perpendicular to the plane x - 2y + z = 1?
• How to find the point where the line x = –1 – t, y = 2 + t, z = 1+ t intersects the plane 3x + y + 3z = 1 ?
• Question #9eda6
• How do you find the equations of the tangents to that curve #x=3t^2 + 1# and #y=2t^3 + 1# that pass through point (4,3)?
• Question #6fe41
• Consider the point #P(3,−5, 1)# and the line #L ∶ x = 2t − 1 , y = −t + 2 , z = −2t; −∞ < t < ∞#. a. Find the equation of the plane passing through P perpendicular to L. b. Find the equation of the plane passing through P and containing L?
• Consider the line which passes through the point P(-1, -5, 4), and which is parallel to the line x=1+5t y=2+5t z=3+5t. How do you find the point of intersection of this new line with each of the coordinate planes?
• How do you find parametric equations for the line through (2, 4, 6) that is perpendicular to the plane x − y + 3z = 7?
• How do you find vector parametric equation for the line through the point P=(−4,−5,3) perpendicular to the plane 3x−4y+3z=−1?
• How do you get a initial and terminal point given #x=cos(pi-t)#, #y=sin (pi-t)#, #0<=t<=1#?
• How do you graph parametric equations x(t)=3t and y(t)=2-2t on [0,1]?
• How do you find the range given #x=t^2-4# and #y=t/2# for #-2 <= t <= 3#?
• How do you find the range given x=3-2t and y=2+3t for -2 ≤ t ≤ 3?
• Consider the parametric equation: #x = 15(cos(theta) + (theta)sin(theta))# and #y = 15(sin(theta) - (theta)cos(theta))#, What is the length of the curve for #theta = 0# to #theta = pi/8#?
• A curve is given by the parametric equations: #x=cos(t) , y=sin(2t)#, how do you find the cartesian equation?
• How do you find a vector equation and parametric equations for the line segment that joins P to Q where P(-7, 2, 0), Q(3, -1, 2)?
• What is the parametric equation of the line through (1,1,1) that is parallel to i+j+k?
• How do you find a vector equation and parametric equations in t for the line through the point and perpendicular to the given plane. (P0 corresponds to t = 0.) P0 = (5, 0, 8) x + 2y + z = 9?
• How do you find parametric equations and symmetric equations for the line through t0 and parallel to the given line t0 = (4, -2, 4) and x + 1 = y/2 = z + 5?
• How do you find the parametric equations for the line through the point P = (2, -2, -1) that is perpendicular to the plane 1x + 3y - 2z = 1?
• How do you determine scalar, vector, and parametric equations for the plane that passes through the points A(1,-2,0), B(1,-2,2), and C(0,3,2)?
• How do you find the set of parametric equations for the line in 3D described by the general equations x-y-z=-4 and x+y-5z=-12?
• How do you find the set of parametric equations for the line through the point P(2,-1,0) which is perpendicular to the plane described by the general equation -x+z=2?
• Given #y=(x/5)^2# how do you derive a parametric equation?
• Given #x^2 + (y – 2)^2 = 4 # how do you derive a parametric equation?
• What is parametric equation of the line created by the intersecting planes x = 2 and z = 2?
• A curve in the xy-plane is defined by the parametric equations #x = t^3 + 2# and #y = t^2 - 5t# how do you find the slope of the line tangent to the curve at the point where x = 10?
• How do you find parametric equation for given curve: Line of slope 8 through (-4,9)?
• How do you find parametric equation for given curve #y²=4ax#?
• How do you find the parametric equation for the line which pass by two points p1=(1,-2,1) p2=(0,-2,3)?
• How do you determine the vector and parametric equations for the plane through point (1, -2,3) and parallel to the xy-plane?
• Do the parametric equations #x = 3t^3 + 7#, #y = 2 - t^3#, #z = 5t^3 + 1# determine a line?
• How do you convert the parametric equations into a Cartesian equation by eliminating the parameter r: #x=(r^2)+r#, #y=(r^2)-r#?
• How do you convert #x^2 + y^2 = 49# into parametric equations?
• How do you find parametric equations for the line which passes through the point (1,−2,3) and is parallel to both of the planes 3x + y + 5z = 4 and z = 1 − 2x?
• The surface #z=xsqrt(x+y)# intersects the plane y=3 along a curve c, how do you find the parametric equations for the tangent line to this curve at the point P(1,3,2)?
• How do you find the parametric equations for the line through the point P = (4, -4, 1) that is perpendicular to the plane 3x + 1y - 4z = 1?
• How do you find the parametric equations of the line of intersection of the planes x+2z=0 and 2x-3y+4?
• How do you find parametric equation for the line through the point P(-7,-3,-6) and perpendicular to the plane -2x + 2y + 6z =3?
• How do you determine the parametric equations of the path of a particle that travels the circle: #(x−3)^2+(y−1)^2=9# on a time interval of #0<=t<=2#?
• The curve given by the parametric equations #x=16 - t^2#, #y= t^3 - 1 t# is symmetric about the x-axis. At which x value is the tangent to this curve horizontal?
• How do you write the parametric equations represent the ellipse given by #x^2/9 + y^2/81=1#?
• How do you write an equation in slope-intercept form of the line with parametric equations: x=2+3t and y=4+t?
• How do you find a vector parametric equation r(t) for the line through points P=(-3,-1,1) and Q = (-8,-4,5) If r(6) = P and r(10) = Q?
• How do you find parametric equations for the tangent line to the curve with the given parametric equations at the point #( 1, 4, 4)#. #x = cos(t), y = 4e^8t, z = 4e^ -8t#?
• How do you write a vector equation and a parametric equation for each line: the line through A(1,-3,1) and parallel to vector u=(2,-2,1)?
• How do you write a vector equation and a parametric equation for each line: the line through A(3,0,4) and parallel to the x-axis?
• How do you write a vector equation and a parametric equation for each line: the line through A(-1,2,1) and B(1,2,1)?
• How do you find the parametric and symmetric equation of the line passing through the point (2,3,4) and perpendicular to the plane 5x+6y-7z=20?
• How do you find the angle between the planes 2x+5y-z=6 and 3x-2y+6z=10?
• How do you give parametric equations for the line through (1, 3, -5) that is perpendicular to the plane #2x -3y +4z = 11#?
• How do you find the parametric equations for the tangent line to the curve #x=t^4−1#, #y=t^2+1#, #z=t^3# at the point (15, 5, 8)?
• How do you find parametric equations for the line of intersection of the planes 2x + 5z + 3 = 0 and x -3y + z + 2 = 0?
• How do you find the parametric equations of the line that passes through #A=(7,-2,4)# and that is parallel to the line of intersection of the planes #4x-3y-z-1=0# and #2x+4y+z-5=0#?
• A curve C is defined by the parametric equations: #x=t^2# and #y = t^3-3t#, how do you show that C has two tangents at the point (3,0) and find their equations?
• How do you find the equations of tangent lines at the point where the curve crosses itself #x=t^2-t# and #y=t^3-3t-1#?
• How do you find two different sets of parametric equations for the given rectangular equation y = 1/x?
• How do you find the parametric equation through the point (6, 0, 10) and parallel to the plane -3x+2y-4z = 0?
• Eliminating the parameter in the parametric equations x = 5 - 3t, y = 2+t yields what equation?
• Given the parent function #f(x) = x^2#, how do you write a set of parametric equations to represent the function?
• Let #x = e^t + 3# and #y = e^(2t)+6e^t+9# how do you eliminate the parameter and write y in terms of x?
• How do you write the cartesian equation for x = t - 2 and y = -(t²) + t + 1?
• Let l be the line that passes through the point P=(−5,−7,−1) and is perpendicular to the plane 8x−6y−1z=15, how do you find the parametric equations?
• How do you convert #(y = 2 + x)# to parametric equation?
• How do you find parametric equations for the tangent line to the curve with the given parametric equations at the specified point #x = 1+10 * sqrt(t)#, #y = t^5 - t#, and #z=t^5 + t# ; (11 , 0 , 2)?
• How do you find parametric equations for the line of intersection of two planes 2x - 2y + z = 1, and 2x + y - 3z = 3?
• How do you find the equation of the tangent line to the curve given by parametric equations: #x=1+(1/t^2)#, # y=1-(3/t)# at the point when t=2?
• How do you write the corresponding rectangular equation by eliminating the parameter given x=3t-1, y=2t+1?
• How do you write the corresponding rectangular equation by eliminating the parameter #x = t^2 + t# and #y = t^2 - t#?
• How do you find parametric equations and symmetric equations for the line through the points (1, 3, 2) and ( -4, 3, 0)?
• How do you find the (shortest) distance from the point P(1, 1, 5) to the line whose parametric equations are x = 1 + t, y = 3 - t, and z = 2t?
• Consider the parametric equation #x = 9(cost+tsint)# and #y = 9(sint-tcost)#, What is the length of the curve for #t= 0# to #t=3pi/10#?
• How do you find the parametric equations for the intersection of the planes 2x+y-z=3 and x+2y+z=3?
• How do you convert each parametric equation to rectangular form: x = t - 3, y = 2t + 4?
• How do you convert each parametric equation to rectangular form: #x = t^(3/2) + 1#, #y = sqrt{t}#?
• How do you combine the parametric equations into one equation relating y to x given x=4cost and y=9sint?
• How do you find the equation of the tangent line for the curve given by x = 2t and #y = t^2 + 5# at the point where t = 1?
• How do you find parametric equations for the line through the point (0,1,2) that is perpendicular to the line x =1 + t , y = 1 – t , z = 2t and intersects this line?
• How do you find a parametric equation for a particle moving twice counter-clockwise around the circle #(x-2)^2 + (y+1)^2 = 9# starting at (-1,-1)?
• How do you find two difference parametric equations for the rectangular equation y=8x-7?
• Consider the parametric equations x = 3t - 5 and y = 2t + 3 how do you eliminate the parameter to find a Cartesian equation of the curve?
• How do you find the parametric equations for the rectangular equation #x^2+y^2=16#?
• How do you find the parametric equations for the line through the point (2,3,4) and perpendicular to the plane 3x + 2y -Z = 6?
• How do you find parametric equations and symmetric equations for the line through #(3, −2, 5)# and parallel to the line #x + 3 = y/2 = z − 2#?
• How do you show that the curve x=cos t , y= sin t cos t has two tangents at (0,0) and find their equations?
• How do you find parametric equations to represent the line segment from (-3,2) to (1,-8)?
• How do you change the parametric equation to cartesian equation #x = t^2 - 1# and #y = t^3#?
• How do you find parametric equations for the line through P-naught=(3,-1,1) perpendicular to the plane 3x+5y-7z=29?
• Given Parametric equations: #x = 2(t)^2# and y = 4t how do you find the cartesian equation?
• How do you find parametric equations for the path of a particle that moves along the #x^2 + (y-3)^2 = 16# once around clockwise, starting at (4,3) 0 ≤ t ≤ 2pi ?
• How do you find parametric equations for the path of a particle that moves along the #x^2 + (y-3)^2 = 16# Three times around counterclockwise, starting at (4,3) 0 ≤ t ≤ 6pi?
• How do you find parametric equations for the path of a particle that moves along the #x^2 + (y-3)^2 = 16# Halfway around counterclockwise, starting at (0,7). 0 ≤ t ≤ pi?
• How do you write parametric equations for the curve that polar equation #r = 3cos(theta)#?
• A line is defined by the parametric equations: x = cos2t and #y = sin^2t# how do you find the cartesian equation of the line?
• How do you find the vector equation and parametric equations for the line through# (0, 14, -10)# and parallel to the line:#x = -1+2t, y = 6-3t, z = 3+9t#?
• Given x = 2 cot t and #y = 2 sin^2 t# for #0<t<= pi/2# how do you find the cartesian equation for this curve and state the domain?
• How do you rewrite the two parametric equations’ as one Cartesian equation x = sec(t), y = tan(t), #-pi/2<t<pi/2#?
• How do you find the Cartesian equation from given parametric equations #x = (2t )/ (1+t^4)# and #y = (2t^3) / (1 + t^4)#?
• How do you find parametric equations for the path of a particle that moves around the given circle #x^2 + (y – 2)^2 = 4# clockwise, starting at (2, 2)?
• The motion of the particle is given parametrically by #x(t)=3t^2-3#, #y(t)=2t^2# for t is greater than or equal to 0, how do you find the speed of the particle at t=1?
• Given x(t)=3sin(t) - 3, y(t)=t-1 for 0 is less than or equal to t is less than or equal to 2pi How do you find the position of the particle at t=3?
• Given x(t)=3sin(t) - 3, y(t)=t-1 for 0 is less than or equal to t is less than or equal to 2pi How do you find the velocity of the particle at t=3?
• Given x(t)=3sin(t) - 3, y(t)=t-1 for 0 is less than or equal to t is less than or equal to 2pi How do you find the speed of the particle at t=3?
• What is #r sin theta = 5# in #(x,y)# coordinates ?
• Question #cad9c
• How do you convert parametric equation to cartesian x = t - 2 and y = -(t²) + t + 1?
• What does the graph #r = sqrt(sintheta)# look like in plane polar coordinates? How do you graph it?
• How do you find the Cartesian equation of the curve with parametric equations #x=2cos(3t)#and #y=2sin(3t)#, and determine the domain and range of the corresponding relation?
• Question #71d19
• What is the area bounded by the parametric equations? : # x=acos theta # and # y=bsin theta #
• How would you solve something like #asint=bt# or #acost=bt# for #t#?
• Question #df769
• Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter?
• 19. "Describe the motion of a particle with position (#x,y#) as #t# varies in the given interval" ?
• Solve for #dy/dx#?