Find the equation of the circle whose radius is 4 and which is concent

1.	Find the equation of the circle whose radius is 4 and which is concentric with the circle x2 + y2 + 2x – 6y = 0
Answer» x² + y² + 2x – 6y = 0 …(1) Here 2g = 2 ⇒ g = 1, 2f = -6 ⇒ f = -3 Centre of the circle = (-g, -f) = (-1, 3) Since the required circle is concentric with (1), its centre is also (-1, 3). ∴ The equation of the circle whose centre is (-1, 3) and radius 4 is (x + 1)² + (y – 3)² = 4² ⇒ x² + y² + 2x – 6y – 6 = 0

Find the equation of the circle whose radius is 4 and which is concentric with the circle x2 + y2 + 2x – 6y = 0

Answer»

x² + y² + 2x – 6y = 0 …(1)

Here 2g = 2 ⇒ g = 1, 2f = -6 ⇒ f = -3

Centre of the circle = (-g, -f) = (-1, 3)

Since the required circle is concentric with (1), its centre is also (-1, 3).

∴ The equation of the circle whose centre is (-1, 3) and radius 4 is

(x + 1)² + (y – 3)² = 4²

⇒ x² + y² + 2x – 6y – 6 = 0