Question

The two circles $x^2+y^2=ax$ and
$x^2+y^2=c^2(c>0)$ touch each other if :-

• A. $2|a|=c$
• B. $|a|=c$
• C. $a=2c$
• D. $|a|=2c$

Answer 1

The correct option is B $|a|=c$

Let $c_1,c_2$ be the center of two circles mentioned.

$c_1=(\frac{a}{2},0)$

$c_2=(0,0)$

$r_1=\frac{a}{2}$, $r_2=c$

$\Rightarrow c_1{c}_2=r_2-r_1$

$\Rightarrow \frac{a}{2}=c-\frac{a}{2}$

$\Rightarrow a=c$

$\Rightarrow |a|=c$

Hence, option 'B' is correct.