Question

Find the centre and radius of the circle.

(x + 2) (x – 5) + (y – 2) (y – 1) = 0

Answer 1

Equation of the circle is (x + 2) (x – 5) + (y – 2) (y – 1) = 0

x² – 3x – 10 + y² – 3y + 2 = 0

x² + y² – 3x – 3y – 8 = 0

Comparing this with x² + y² + 2gx + 2fy + c = 0

We get 2g = -3, 2f = -3, c = -8

g = `(-3)/2,` f = `(-3)/2`, c = - 8

Centre (-g, -f) = `(3/2, 3/2)`

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

= `sqrt(9/4 + 9/4 + 8)`

`= sqrt(18/4 + 8)`

`= sqrt(9/2 + 8)`

`= sqrt((9+16)/2)`

`= sqrt(25/2)`

`= 5/sqrt2`