Question

Write the parametric equations of the circle: 

x² + y² + 2x − 4y − 4 = 0

Answer 1

Given equation of the circle is

x² + y² + 2x − 4y − 4 = 0

∴ x² + 2x + y² – 4y – 4 = 0

∴ x² + 2x +1 – 1 + y² – 4y + 4 – 4 – 4 = 0

∴ (x² + 2x + 1 ) + (y² – 4y + 4) – 9 = 0

∴ (x + 1)² + (y – 2)² = 9

∴ (x + 1)² + (y – 2)² = 3²

Comparing this equation with

(x – h)² + (y – k)² = r², we get

h = – 1, k = 2 and r = 3

∴ The parametric equations of the circle in terms of θ are

x = h + r cos θ and y = k + r sin θ

∴ x = – 1 + 3cos θ and y = 2 + 3sin θ.