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Question

The diameter of \(16x^2- 9 y^2 = 144\) which is conjugate to x = 2y, is

A
y=16x9
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B
y=32x9
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C
x=16y9
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D
x32y9
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Solution

The correct option is B y=32x9

Diameters y=m1xandy=m2x are conjugate diameters of the hyperbola
x2a2y2b2=1, if m1m2=b2a2 .
Here, a2=9,b2=16 and m1=12
m1m2=b2a212(m2)=169
m2=329
Thus, the required diameter is y=32x9

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