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Question

The length of the latus rectum of the parabola 25[(x2)2+(y4)2]=(4x3y+12)2 is

A
165
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B
125
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C
85
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D
45
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Solution

The correct option is A 165
The given equation of the parabola can be written as
(x2)2+(y4)2=(4x3y+12(4)2+(3)2)2
The coordinates of focus are (2,4) and the equation of directrix is 4x3y+12=0.
The distance of the focus from the directrix
=∣ ∣ ∣4(2)3(4)+1242+(3)2∣ ∣ ∣=85
The length of latus rectum
=2× distance of the focus from the directrix
=2×85=165

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