Question

Find the centre and radius of the circle.

5x² + 5y²+ 4x – 8y – 16 = 0

Answer 1

To make coefficient of x² unity, divide the equation by 5 we get,

`x^2 + y^2 + 4/5 x - 8/5 y - 16/5 = 0`

Comparing the above equation with x² + y² + 2gx + 2fy + c = 0 we get,

2g = `4/5`, 2f = `-8/5`, c = `(- 16)/5`

∴ g = `2/5`, f = `- 4/5`, c = `(-16)/5`

Centre = (-g, -f) = `((-2)/5, 4/5)`

Radius = `sqrt("g"^2 + "f"^2 - "c"^2)`

`= sqrt((2/5)^2 + ((-4)/5)^2 - ((-16)/5))`

`= sqrt(4/25 + 16/25 + 16/5)`

`= sqrt((4 + 16 + 16 xx 5)/25)`

`= sqrt((20 + 80)/25)`

`= sqrt(100/25)`

`= sqrt4` = 2