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Question

Find the equation of a normal to the ellipse x216+y29=2 at the point (4, 3).


A

3x + 4y = 24

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B

4x - 3y = 7

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C

4x + 3y = 25

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D

3x - 4y = 0

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Solution

The correct option is B

4x - 3y = 7


In the last topic we learned how to write the equation of tangent once the points are given.
So the tangent at (4, 3) to x216+y29=2 will be x×416+y×39=2x4+y3=2Slope of this line=34Slope of normal=43
We can now write the equation of normal y - 3 = 43(x4)
4x3y=169=7
Using formula
The equation of normal at (x1,y1) to the ellipse x2a2+y2b2=1 is given by a2xx1b2yy1=a2b216×x49×y3=1694x3y=7
We can see that using formula saves a lot time. We recommend you to remember it.


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