Question

Find the equation of the circle whose centre is (-3, -2) and having circumference 16π.

Answer 1

Circumference, 2πr = 16π

⇒ 2r = 16

⇒ r = 8

Equation of the circle when centre and radius are known is (x – h)² + (y – k)² = r²

⇒ (x + 3)² + (y + 2)² = 8²

⇒ x² + 6x + 9 + y² + 4y + 4 = 64

⇒ x² + y² + 6x + 4y + 13 = 64

⇒ x² + y² + 6x + 4y – 51 = 0