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Question

Tangents are drawn from a point P(6,5) to the ellipse x225+y216=1 touching the ellipse in the points Q and R. The angle between PQ and PR is

A
45
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B
60
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C
90
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D
30
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Solution

The correct option is D 90
Solution -
Let θ is the angle between the tangents

Let a line y=mx+c is tangent to

the ellipse x225+y216=1

then c=25m2+16

y=mx+25m2+16

It passes through (6,5)

(56m)2=(25m2+16)

36m2+5125m=25m2+16

11m2125m11=0

m1m2=1111=1

Tangents are perpendicular

θ=90

C is correct

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