Question

The point (5,-6) lies on a circle and the center of the circle is at the point (5,-8).

What is the equation of this circle?
A.
(x - 5)2 + (y + 8)2 = 4
B.
(x - 8)2 + (y - 5)2 = 4
C.
(x + 5)2 + (y - 8)2 = 4
D.
(x - 8)2 - (y - 5)2 = 2

Answer 1

A.

(x - 5)^2 + (y + 8)^2 = 4

Explanation:

The equation for a circle in center radius form is

(x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center and r is the radius

We need to determine the radius, from the two points which is the distance

d = sqrt( (x2-x1)^2 + (y2-y1)^2)

= sqrt( (5-5)^2+( -8--6)^2)

= sqrt(0+ (-8+6)^2)

= sqrt( 0+(-2)^2)

= sqrt(4)

= 2

The radius is 2 and the center is (5,-8)

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

(x-5)^2 + (y+8)^2 = 4