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Question

If parabola y2=λx and 25[(x3)2+(y+2)2]=(3x4y2)2 are equal , then value of λ is

A
9
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B
3
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C
7
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D
6
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Solution

The correct option is C 6
Two parabolas are equal if the length of their latus rectum are equal.
Length of the latus rectum of y2=λx is λ.
The equation of the second parabola is
25{(x3)2+(y+2)2}=(3x4y2)2
(x3)2+(y+2)2=|3x4y2|32+42
Here focus is (3,2) and equation of the directrix is 3x4y2=0
Therefore, length of the latus rectum =2× distance between focus and directrix
=2∣ ∣ ∣3×34×(2)232+(4)2∣ ∣ ∣=6
Thus, the two parabolas are equal, if λ=6.

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