Question

The two circles $x^2+y^2=ax$ and $x^2+y^2=c^2\left(c>0\right)$ touch each other, if $\left|\frac{c}{a}\right|$ is equal to

• A. $2$
• B. $\frac{1}{2}$
• C. $1$
• D. None of these

Answer 1

Answer: (C)

The two circles touch each other internally as shown in the figure below

For the circle $x^2+y^2-2ax=0$ , the centre is at $\left(\frac{a}{2},0\right)$ and radius is $\frac{a}{2}$ units.
Also, the circle is passing through the origin.
For the circle $x^2+y^2=a^2$ , the centre is at $\left(0,0\right)$ and radius is $c$ units
From the figure,
$c=2\left|\frac{a}{2}\right|=\left|a\right|$
Hence, $\left|\frac{c}{a}\right|=1$