Question

Write the parametric equations of the circles: 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 + 3 cos θ and y = 2 + 3 sin θ