Question:
Let the latus ractum of the parabola $y^{2}=4 x$ 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 $\mathrm{C}_{1}$ and $\mathrm{C}_{2}$ is:
Correct Option: 1,
Solution:
Length of latus rectum $=4$
$\mathrm{DB}=2$
$C_{1} B=\sqrt{\left(C_{1} D\right)^{2}-(D B)^{2}}=4$
$\mathrm{C}_{1} \mathrm{C}_{2}=8$
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