Question

Determine the equation of the circle with center ( 8 , 5 ) (8,5) containing the point ( − 4 , 21 ) (−4,21).

Answer 1

The equation of the circle is (x - 8)² + (y - 5)² = 20²

Explanation:

Equation of the circle: (x-h)² + (y-k)² = r²

where (h,k) is the center of the circle

Since we're given a point, we can then get the radius of the circle through the distance formula

`d = √((x_2-x_1)^2 + (y_2-y_1)^2) \\d = √((8-(-4))^2+ (5-21)^2) \\d = √((8+4)^2+(-16)^2) \\d = √(12^2 + 256) \\d = √(144+256)\\ d = √(400)\\ d = 20`

r = d

r = 20

Find the equation of the circle

(x - 8)² + (y - 5)² = 20²