Let latus ractum of parabola y ^{2}=4 x be common chord to circles C _{1} and C _{2} each of them ha

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10-1.Circle and System of Circles

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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 $C _{1}$ and $C _{2}$ is

A

$8$

B

$4 \sqrt{5}$

C

$12$

D

$8 \sqrt{5}$

(JEE MAIN-2020)

Solution

Length of latus rectum $=4$

$DB =2$

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

$C _{1} C _{2}=8$

Standard 11

Mathematics

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