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Find the equation of the circle whose center and radius are given.

center ( 5, 6), radius = 3

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AFOKE88id AFOKE88id · Answer 1

The equation of the circle whose center and radius are given as center ( 5, 6), radius = 3 is; x² + y² - 10x - 12y + 52 = 0

We know that the general form of equation of a circle whose center is (h, k) and radius is r is expressed as;

(x - h)² + (y - k)² = r² --- (1)

We are given;

Center coordinate; (h, k) = (5, 6)

radius; r = 3

Plug in the values of h = 5 , k = 6 and r = 3 into the equation to get;

(x - 5)² + (y - 6)² = 3²

Expanding the equation gives;

x² - 10x + 25 + y² - 12y + 36 = 9

x² + y2 - 10x - 12y + 52 = 0

Thus the equation of the circle whose center and radius are given as center ( 5, 6), radius = 3 is; x² + y² - 10x - 12y + 52 = 0

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