Question

Let the latus ractum of the parabola $y^{2}=4x$ be the common chord to the circles $C _{1}$ and $C _{2}$ each of them having radius $2 \sqrt{5}$. Then, the distance between the centres of the circles $C _{1}$ and $C _{2}$ is:

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

Answer 1

The Correct Option is A

Length of latus rectum = 4

$DB =2$
$C _{1} B =\sqrt{\left( C _{1} D \right)^{2}-( DB )^{2}}=4$
$C _{1} C _{2}=8$