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Question

The equation of the normal to the ellipse x218+y28=1 at the point (3,2) is .

A
3x - 2y = 5
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B
3x + 2y = 5
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C
2x - 3y = 5
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D
2x + 3y = 5
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Solution

The correct option is A 3x - 2y = 5
The given equation of ellipse is x218+y28=1.
Differentiating w.r.t x, we get:
2x18+2y8dydx=1dydx=4x9ySlope of a normal=dxdy=9y4xSlope of the normal at the point (3,2)=9(2)4(3)=32the equation of the normal will be:y2=32(x3) or 3x2y=5

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