Question

If the circles $x^2+y^2=a^2$ and $x^2+y^2-2gx+g^2-b^2=0$ touch each other externally, then

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

For Second circle: $x^2+y^2-2gx+g^2-b^2=0$
Centre $=C_2(-h,-k)=(g,0)$ and
radius $=r_2=\sqrt{h^2+k^2-c}$
$=\sqrt{(-g{)}^2+0^2-g^2+b^2}$
$=\sqrt{g^2-g^2+b^2}$
$=\sqrt{b^2}$
$\therefore r_2=b$
Since, the two circles touch each other externally,
So, $C_1{C}_2=r_1+r_2$
$\Rightarrow \sqrt{(g-0{)}^2+(0-0{)}^2}=a+b$
$\Rightarrow \sqrt{g^2}=a+b$
$\therefore g=a+b$