The points
on the curve 9*y* ^{2} = *x* ^{3}, where the
normal to the curve makes equal intercepts with the axes are

(A) (B)

(C) (D)

The
equation of the given curve is 9*y*^{2} = *x*^{3}.

Differentiating
with respect to *x*, we have:

The slope of the normal to the given curve at point is

∴ The equation of the normal to the curve at is

It is given that the normal makes equal intercepts with the axes.

Therefore, We have:

Also, the pointlies on the curve, so we have

From (i) and (ii), we have:

From (ii), we have:

Hence, the required points are

The correct answer is A.

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