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Question

Find the points on the curve 2a2y=x33ax2 where the tangent is parallel to xaxis.

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Solution

A]2a2y=x33ax2

Let (x1,y1) be the required points.
slope of x axis is o.
as point lies on the curve

2a2y1=x313ax21 ...(1)
Differentiating,

2a2dydx=3x26ax

dydx=3x26ax2a2

slope of taangent at (x1,y1)dydx=3x216ax12a2

Now3x216ax12a2=0

3x21+6ax1=0

x1(3x16a)=0

x1=0 or x1=2a

Also, 2a2y1=0 or 2a2y1=8a312a3

y1=0 or y1=2a points(0,0)(2a,20)

1182475_1293312_ans_71ebfc7236dc4ff9b41f50bcc58657d9.jpg

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