Find the standard form for the equation of a circle ?

Question

Find the standard form for the equation of a circle (x-h)2 +(y-k)2=r2

with a diameter that has endpoints (-10,-2) and(6,-2)

Answer 1

Center is the midpoint of the diameter = (-2, -2)

Radius = 8, distance from center to either point.

(x + 2)^2  + (y + 2) ^ 2 = 64

Answer 2

(x-h)²+(y-k)² = r²

(h, k) is the center

r is the radius

The endpoints of the diameter have the same y-coordinate, so the diameter is horizontal and has length (6--10) = 16.

d = 16

r = d/2 = 8

The center of the circle is the midpoint of the diameter, (-2, -2).

The equation of the circle becomes

(x+2)²+ (y+2)² = 64

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