Question

Find the equation of the circle In each of the following cases.

1. Centre (0, 2) and radius 2.

2. Centre (-2, 3) and radius 4.

3. Center (\(\frac{1}{2}, \frac{1}{4}\)) and radius \(\frac{1}{12}\).

Answer 1

1. The equation of the circle is

(x – 0)² + (y – 2)² = 2²

⇒ x² + y² – 4y + 4 = 4

⇒ x² + y² – 4y = 0.

2. The equation of the circle is

(x + 2)² + (y – 3)² = 4²

⇒ x² + 4x + 4 + y² – 6y + 9 = 16

⇒ x² + y² + 4x – 6y – 3 = 0.

3. The equation of the circle is

⇒ 144x² + 36 – 144x + 144y² + 9 – 72y = 1

⇒ 144x² + 144y² – 144x – 72y + 44 = 0

⇒ 36x² + 36y² – 36x – 18y + 11 = 0.