Question #3ddb7

2 Answers
Jan 14, 2018

( (20sqrt17)/17, (-5sqrt17)/17),( (-20sqrt17)/17, (5sqrt17)/17)

Explanation:

finding the equation of the circle:

the general equation of a circle centered at the origin is x^2+y^2=r^2,
where r is the radius of the circle.

if the radius is 5, r^2 = 25.

the equation of the circle is therefore x^2+y^2=25.

finding points of intersection:

solve simultaneous equations x^2+y^2=25 and y=-x/4.

(here, it is easier to insert y than x)

x^2+y^2=25
x^2+(-x/4)^2=25

(-x/4)^2 = x^2/16

x^2+x^2/16 =25

(16x^2)/16 + x^2/16 = 25

(17x^2)/16 = 25

17x^2 = 25 * 16 = 400

x^2 = 400/17

x = sqrt(400/17) = 20/sqrt17 or -20/sqrt17

x = (20sqrt17)/17 or (-20sqrt17)/17

y = -x/4 = (-5sqrt17)/17 or (5sqrt17)/17

coordinates: ( (20sqrt17)/17, (-5sqrt17)/17),( (-20sqrt17)/17, (5sqrt17)/17)

Jan 14, 2018

P_1: (4.85, -1.21)
P_2: (-4.85, 1.21)

Explanation:

Set radius = r = 5

The equation of the circle:

x^2 + y^2 = r^2

x^2 + y^2 = 25

The equation of the line:

y = -x/4

Insert equation of the circle in the equation of the line to find the intersection points.

x^2 + y^2 = 25

x^2 + (-x/4)^2 = 25

x^2 + (x^2/16) = 25

(16x^2)/17 = 25

x^2 = (25*17)/16

x = +- sqrt((25*17)/16)

x = +- 4.85

So, the x values are:

x_1 = 4.85

x_2 = -4.85

NOTE: It is important to always put the+- in front of a square root, because both the negative and the positive answer can be correct.

Now, find the y value by plugging the two x values in any of the two equations.

y_1 = -(-4.85)/4 = 1.21

y_2 = -(4.85)/4 = -1.21