Question

The equation of the circle with centre at (-2, -5) and passing through the centre of the given circle x² + y² + 16y + 29 = 0 is ______ 

Options

• x² + y² + 4x + 10y - 21 = 0 

• x² + y² + 4x + 10y - 16 = 0

• x² + y² + 4x + 10y + 21 = 0 

• x² + y² + 4x + 10y + 16 = 0

Answer 1

The equation of the circle with centre at (-2, -5) and passing through the centre of the given circle x² + y² + 16y + 29 = 0 is x² + y² + 4x + 10y + 16 = 0.

Explanation:

The Centre of the given circle is (0, -8).

∴ the required circle passes through (0, -8).

∴ `r = sqrt((0 + 2)^2 + (-8 + 5)^2) = sqrt13`

 Hence, the required equation is

`(x + 2)^2 + (y + 5)^2 = (sqrt13)^2`

⇒ x² + y² + 4x + 10y + 16 = 0