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Question

Find points on the curve x29+y2161 at which the tangents are parallel to x-axis

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Solution

given, x29+y216=1

y216=1x29

116(2ydydx)=2x9

dydx=16x9y

Parallel to xaxis

Given tangent is parallel to xaxis

Slope of tangent=Slope of xaxis

dydx=0

16x9y=0

This is only possible if x=0 (If y=0,16x9×0=)

When x=0

x29+y216=1

09+y216=1

0+y216=1

y2=16

y=±4

Hence the points are (0,4) and (0,4)

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