How do you write the equation for a circle centered at (h,k) = (5,-8) and passing through the point (3,-2)?

1 Answer
Aug 8, 2018

Answer:

#(x-5)^2+(y+8)^2=40#

Explanation:

#"the standard form of the equation of a circle is"#

#color(red)(bar(ul(|color(white)(2/2)color(black)((x-h)^2+(y-k)^2=r^2)color(white)(2/2)|)))#

#"where "(h,k)" are the coordinates of the centre and r"#
#"is the radius"#

#"the radius r is the distance from the centre to the point"#
#"on the circumference"#

#"calculate r using the "color(blue)"distance formula"#

#•color(white)(x)r=sqrt((x_2-x_1)^2+(y_2-y_1)^2)#

#"let "(x_1,y_1)=(5,-8)" and "(x_2,y_2)=(3,-2)#

#r=sqrt((3-5)^2+(-2+8)^2)=sqrt(4+36)=sqrt40#

#(x-5)^2+(y+8)^2=40larrcolor(blue)"is equation of circle"#