Question

Let the latus rectum of the parabola $y^2=4x$ be the common chord to the circles $C_1$ and $C_2$ each of them having radius $2\surd 5$. Then, the distance between the centres of the circles $C_1$ and $C_2$ is

• A. $8$
• B. $8\sqrt{5}$
• C. $4\sqrt{5}$
• D. $12$

Answer 1

The correct option is A

$8$

Explanation for the correct option:

Finding the distance between the centres of the circles:

$$\begin{gathered} C_1{C}_1=2C_{1}A \\ {\left(C_{1}A\right)}^2+4={(2\surd 5)}^2 \\ {C}_{1}A=4 \\ {C}_1{C}_2=8 \end{gathered}$$

Therefore, the correct answer is option (A).