Question

Let the point at which the circle passing through $\left(0,0\right)$ and $\left(1,0\right)$ touches the circle $x^{2}+y^{2}=9$ is $P\left(h , k\right)$ , then $\left|k\right|$ is equal to

• A. $\sqrt{5}$
• B. $2\sqrt{2}$
• C. $\sqrt{6}$
• D. $\sqrt{7}$

Answer 1

Answer: (B)

From the figure,
for the small circle, the radius is $\frac{3}{2}$ units and the centre is $\left(\frac{1}{2} , \lambda \right)$
Therefore,
$\sqrt{\left(\frac{1}{2}\right)^{2} + \left(\lambda \right)^{2}}=\frac{3}{2}\Rightarrow \lambda =\pm\sqrt{2}$
Since, $OP$ is the diameter of the circle,
$\Rightarrow P=\left(1 , \pm 2 \sqrt{2}\right)\Rightarrow \left|k\right|=2\sqrt{2}$