The length of latus rectum of the parabola (x-2 a)^2+y^2=x^2 is: - Vidyadip

MCQ

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

A
2a
B
3a
C
6a
✓
4a

✓

Answer

Correct option: D.

4a

4a

Solution:
$\text { We have }(x-2 a)^2+y^2=x^2$
$\Rightarrow x^2-4 a x+4 a^2+y^2=x^2$
$\Rightarrow y^2=4 a x-4 a 2=4 a(x-a)$
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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