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Question

The eccentricity of the conic 4(2yx3)29(2x+y1)2=80 is

A
23
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B
32
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C
2
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D
133
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Solution

The correct option is D 133
Here, 2yx3 and 2x+y1 are perpendicular to each other.
Therefore, the equation of the conic can be written as
4×5(2yx322+12)29×5(2x+y122+12)2=80
4(2yx35)29(2x+y15)2=16

On putting 2yx35=X and 2x+y15=Y, the given equation can be written as
4X29Y2=16
X24Y2(4/3)2=1
This is a Hyperbola.
Therefore, eccentricity is given by,
e=1+16/94
=133

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