Question

Equation of circle with center (-a, -b) and radius $\sqrt{a^2-b^2}$ is.

• A. $x^2+y^2-2ax-2by-2b^2=0$
• B. $x^2+y^2-2ax-2by+2a^2=0$
• C. $x^2+y^2+2ax+2by+2b^2=0$
• D. $x^2+y^2-2ax-2by+2b^2=0$

Answer 1

Answer: (C)

$x^2+y^2+2ax+2by+2b^2=0$

Fact: equation of circle with centre $(h,k)$ and radius $r$ is given by

$(x-h{)}^2+(y-k{)}^2=r^2$

Hence equation of circle with centre $(-a,-b)$ having radius $\sqrt{a^2-b^2}$ is given by,

$(x+a{)}^2+(y+b{)}^2=a^2-b^2$

$\Rightarrow x^2+y^2+2ax+2by+a^2+b^2=a^2-b^2$

$\Rightarrow x^2+y^2+2ax+2by+2b^2=0$