Question

Two circles $x^2+y^2+ax=0$ and $x^2+y^2=c^2$ touches each other internally if

• A. $a=0$
• B. $a-c=0$
• C. $a^2=c^2=0$
• D. None of these

Answer 1

The correct option is B $a-c=0$

$C_1(-\frac{a}{2},0)$ and $r_1=\frac{a}{2}$

$C_2(0,0)$ and $r_2=c$

Since, circles touch each other, the distance between $C_1{C}_2=|r_1-r_2|$

$\Rightarrow \left|\frac{a}{2}\right|=|\frac{a}{2}-c|$

$\Rightarrow c=0ora-c=0$

So, option B is correct.