# 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 $2\sqrt{5}.$ Then, the distance between the centres of the circles $C_{1}$ and $C_{2}$ is : Option: 1   Option: 2 Option: 3 Option: 4

Length of latus rectum = 4

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

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