Question

The points J(-8,9) and K(-2,-5) are endpoints of a diameter of circle C. Which equation represents circle C?

A.
(x − 5)2 + (y + 2)2 = 58
B.
(x − 5)2 + (y + 2)2 = 232
C.
(x + 5)2 + (y − 2)2 = 58
D.
(x + 5)2 + (y − 2)2 = 232

Answer 1

The Answer is C

Explanation:

The center of circle C is the midpoint of the diameter JK. We can find the coordinates of the center using the midpoint formula:

x-coordinate of center = (x-coordinate of J + x-coordinate of K)/2 = (-8 - 2)/2 = -5

y-coordinate of center = (y-coordinate of J + y-coordinate of K)/2 = (9 - 5)/2 = 2

So, the center of circle C is (-5, 2). The radius of the circle is half the distance between J and K:

radius = 1/2 * √[(x-coordinate of K - x-coordinate of J)2 + (y-coordinate of K - y-coordinate of J)2]

radius = 1/2 * √[(-2 - (-8))2 + (-5 - 9)2] = √58

Using the standard form equation of a circle with center (h,k) and radius r:

(x - h)2 + (y - k)2 = r2

Substituting the values for h, k, and r, we get:

(x + 5)2 + (y - 2)2 = 58

So, the equation that represents circle C is option C: (x + 5)2 + (y - 2)2 = 58.