Write the equation of the circle centered at ( 5 , − 10 ) that passes through ( 7 , − 7 ) .

Answer 1

The equation for a circle is (x-h)^2 + (y-k)^2 = r^2, with the center of the circle located at (h,k), and a radius r.

We can start by plugging in the values we know for the center of the circle:

(x-5)^2 + (y+10)^2 = r^2

For a circle to pass through a point, it must be along the radius of the circle.

We can now plug in the coordinates of that point.

(7-5)^2 + (-7+10)^2 = r^2

(2)^2 + (3)^2 = r^2

(4) + (9) = 13

The final equation of the circle is:

(x-5)^2 + (y+10)^2 = 13