The length of latus rectum of the parabola $(x - 2 a)^{2} + y^{2} = x^{2}$ is

2 a

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3 a

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6 a

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4 a

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Solution

The correct option is C $4 a$
We have, $(x - 2 a)^{2} + y^{2} = x^{2}$
$\Rightarrow x^{2} - 4 a x + 4 a^{2} + y^{2} = x^{2}$
$\Rightarrow y^{2} = 4 a x - 4 a^{2} = 4 a (x - a)$
Comparing it with standard parabola $Y^{2} = 4 b X$
$Y = y, X = x - a, b = a$
We know length of latus rectum of parabola $Y^{2} = 4 b X$ is $4 b$
Hence length of latus rectum of given parabola is $= 4 \times a = 4 a$

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