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Question

On the ellipse 4x2+9y2=1, the points at which the tangents are parallel to the line 8x=9y are

A
(25,15)
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B
(25,15)
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C
(25,15)
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D
(25,15)
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Solution

The correct options are
B (25,15)
D (25,15)
Any point on the ellipse 4x2+9y2=1
(12cosθ,13sinθ)
Slope of the tangent will be,
8x+18ydydx=0dydx=23cosθsinθ
The tangent is parallel to 8x=9y
89=23cosθsinθtanθ=43
So,
cosθ=45,sinθ=35
or
cosθ=45,sinθ=35

Corresponding points will be,
(25,15) and (25,15)

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