Question

Equation of circle with centre $(-a, - b)$ 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)

We know that equation of circle having centre $(h, k)$ and radius $r$ is
$(x-h)^{2}+(y-k)^{2}=r^{2}$.
Here, centre $=(-a,-b)$ and radius
$=\sqrt{a^{2}-b^{2}}$
$\therefore $ Required equation of circle is
$(x+ a)^{2}+(y +b)^{2} =\left(\sqrt{a^{2}-b^{2}}\right)^{2}$
$\Rightarrow x^{2}+a^{2}+2 a x +y^{2}+b^{2}+2 b y=a^{2}-b^{2}$
$\Rightarrow x^{2}+2 a x +y^{2}+2 by+2 b^{2} =0$