Question

Find the equation of a circle with a center at (7,2) and a point on the circle at (-2,-5).

( x - 7 )^2 + ( y - 2 )^2 = sqrt 130
( x + 7 )^2 - ( y + 2 )^2 = sqrt 130
( x - 7 )^2 + ( y - 2 )^2 = 130
( x + 7 )^2 - ( y + 2 )^2 = 130

Answer 1

(x - 7)² + (y - 2)² = 130

Explanation:

The first step is finding the length of the radius.

r² = (2 - -5)² + (7 - -2)²

= 7² + 9²

= 49 + 81

= 130

The general equation of a circle is:

(x - a)² + (y - b)² = r²

Where (a, b) is the coordinate of the center and r is the radius.

∴ The equation of the required circle is;

(x - 7)² + (y - 2)² = 130