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A circle with centre (5,-4) passes through the point (5, ...

A circle with centre (5,-4) passes through the point (5, 0). Find its equation.

A.

x2 + y2 + 10x + 8y + 25 =0

B.

x2 + y2 +10x - 8y - 25 = 0

C.

x2 + y2 - 10x + 8y + 25 =0

D.

x2 + y2 -10x - 8y - 25 = 0

Correct answer is C

(x - h)2 + (y - k)2 = r2

x2 - 2hx + y2 - 2ky + h2 + k2 = r2

x2 - 2(3)x + y2 - 2(-4) y + 52 + (-4)2 = r2

x2 - 10x + y2 + 8y + 25 + 16 = r2

x2 - 10x + y2 + 8y + 41 = r2

at point (5,0)

52 - 10(5) + 02 + 8(0) + 41 = r2 

25 - 50 + 41 = r2

16 = r2 

r = 16 

= 4 

x2 + y2 - 10x + 8y + 25 = 0