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Question

If xa+yb=2 touches the ellipse x2a2+y2b2=1 at a point P, then eccentric angle of P is

A
0o
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B
90o
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C
45o
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D
60o
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Solution

The correct option is C 45o
Equation of tangent in parametric form to an ellipse is
xcosθa+ysinθb=1
Comparing it with given equation
cosθ=12,sinθ=12θ=π4
So the eccentric angle is 45

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