If the diameter of a circle has endpoints p(–10, –2) and q(4, 6), where is the center of the circle, how long is its radius, and what is the equation for the circle?

The center of the circle is midpoint of the diameter:



The radius is equal the distance between C and Q:



An equation of a circle:

(x - a)² + (y - b)² = r²

(a; b) - a coordinates of a center
r - a radius

r = √65; (-3; 2) ⇒ a = -3 and b = 2

subtitute

(x - (-3))² + (y - 2)² = (√65)²

the center: (-3; 2)
the radius: √65
the equation of the circle: (x + 3)² + (y - 2)² = 65