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Question

From the point P(1,5) tangents PQ and PR are drawn to the ellipse x24+y225=1, then the acute angle QOR, where O is the origin, is

A
tan1815
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B
tan1835
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C
tan1158
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D
tan1415
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Solution

The correct option is A tan1815
Equation of chord of contact QR is
T=0
x4+5y25=1
x4+y5=1(1)

Homogenising the given equation we will get OQ and OR
Using Equation (1)
x24+y225=(x4+y5)2
x24+y225=x216+y225+2xy203x216=2xy2015x28xy=0

So,
tanθ=h2aba+btanθ=8215=815
θ=tan1815

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