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Question

If xa+yb=2 touches the ellipse x2a2+y2b2=1, then its eccentric angle θ is equal to

A
0
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B
90
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C
45
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D
60
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Solution

The correct option is C 45
Equation of the tangent at point θ is xacosθ+ybsinθ=1....(1)
Given line is xa.12+yb.12=1....(2)
Since (2) touches the ellipse, (1), (2) represent the same line.
cosθ=12,sinθ=12
θ=45

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