Question

If the point P(x, y) lie on a circle with the center (3, -2) and radius 3 unit, then prove that x² + y² – 6x + 4y + 4 = 0

Answer 1

Let center of circle C(3, -2) and point P(x,y) lie on a circle.

Given : radius of circle CP = 3

⇒ √((x - 3)² + (y + 2)²) = 3

Squaring both sides

⇒ (x – 3)² + (y + 2)² = 9

⇒ x² + 9 – 6x + y² + 4 + 4y = 9

⇒ x² + y² – 6x + 4y + 4 = 0