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Question

Form point P(8,27), tangent PQ and PR are drawn to the ellipse x24+y29=1.If the angle subtended by QR at origin is ϕ, then tanϕ=

A
665
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B
4665
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C
8665
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D
486455
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Solution

The correct option is D 486455

Chord of contact drawn from P(8,27) to the ellipse x24+y29=1 is T=0
2x+3y=1(i)
Now, to get the equation of the pair of lines passing through origin and points Q,R.
Making equation of ellipse homogeneous using equation (i), we get
x24+y29=(2x+3y)2
9x2+4y2=36(4x2+12xy+9y2)
135x2+432xy+320y2=0
QOR=ϕtanϕ=2h2aba+b
tanϕ=22162135×320455
tanϕ=486455

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