Question

Write the equation of a circle with center (6, −2) and contains the point (−5, 9).

Answer 1

(x - 6)² + (y + 2)² = 242

Explanation:

Equation of a circle with center (a, b) and radius r is

(x - a)² + (y - b)² = r²

Given center is at (6, -2) the equation becomes

(x - 6)² + (y - (-2))² = r²

(x-6)² + (y+2)² = r²

Since the circle passes through point (-5, 9), these coordinates must satisfy the above equation.

Plugging in values we get

(-5 -6)² + (9+2)² = r²

Or,

r² = 11² + 11² = 121 + 121 = 242

So the equation of the circle is
(x - 6)² + (y + 2)² = 242