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Question

If the line xa+yb=2 touches the ellipse x2a2+y2b2=1, then the eccentric angle of point of contact is

A
45
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B
90
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C
30
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D
0
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Solution

The correct option is A 45
Let θ be the eccentric angle of the point of contact, then tangent at this point is xcosθa+ysinθb=1
Comparing it with given equation of line xa2+yb2=1, we get
cosθ12=sinθ12=1
cosθ=12 and sinθ=12
θ=45

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