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Question

The points on the curve 9y2=x3, where the normal to the curve makes equal intercepts with the axes are

A
(4,±83)
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B
(4,83)
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C
(4,±38)
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D
(±4,38)
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E
answer required
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Solution

The correct option is A (4,±83)
Let the point on curve be (h,k)
y2=x392y.dydx=19.3x2dydx=x26y
dydx gives slope of curve at given point
dydxat(h,k)=h26k
but this is the slope of tangent and we need slope of normal
As we know that slope of normal× slope of tangent is 1
slope of normal is 6kh2
Given in question that normal makes equal intercepts on axes which means slope of normal is either 1 or 1
6k=h2 and 6k=h2
Now go through the option you will that option A satisfy our equation

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