Equation of circle with centre (-a,-b) and radius `sqrt(a^(2)-b^(2))` is

Options

A. `x^(2)+y^(2)+2ax+2by+2b^(2)=0`
B. `x^(2)+y^(2)-2ax-2by+2b^(2)=0`
C. `x^(2)+y^(2)-2ax-2by-2b^(2)=0`
D. `x^(2)+y^(2)-2ax+2by+2a^(2)=0`

Answer

A

Explanation

We know that, equation of circle having centre (h,k) and radius is `(x-h)^(2)+(y-k)^(2)=r^(2)`
Here, centre `=(a,-b)` and radius `sqrt(a^(2)-b^(2)`
`therefore` Requation of circle is
`(x+a)^(2)+(y-b)^(2)=(sqrt(a^(2)-b^(2)))^(2)`
`rArr x^(2)+a^(2)+2ax+y^(2)+b^(2)+2by=a^(2)-b^(2)`
`rArr x^(2)+2ax+y^(2)+2by+ab^(2)=0`