Write the equation of the circle in standard form. x^2 + y^2 − 6x + 10y + 18 = 0

Question

x^2 + y^2 − 6x + 10y + 18 = 

Answer 1

The standard equation of a circle centered at (h, k) with radius r is (x-h)² + (y-k)² = r².

Rewrite the given equation as

 

x2 - 6x +  (6/2)²  + y2 + 10 y + (10/2)² = - 18 + 9 + 25

(x - 3)² + (y + 5)² = 16

(x - 3)² + (y + 5)² = 4².

 

This is the equation of a circle centered at (3, -5) with radius 4.