Question

Find the equation of the circle with centre (–a, –b) and radius `sqrt(a^2-b^2)`.

Answer 1

The equation of a circle with centre (h, k) and radius r is given as

(x­ – h)² + (y ­– k)² = r²

It is given that centre (h, k) = (-a, -b) and radius (r) = `sqrt(a^2 - b^2)`

Therefore, the equation of the circle is

(x + a)² + (y + b)² = `(sqrt("a"^2 - "b"^2))^2`

= x² + 2ax + a² + y² + 2by + b² 

= a² – b²

= x² +y² + 2ax + 2by + 2b² = 0