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Find the points on the curve 9y2=x3where thenormal to the curve makes equal intercepts with the axis.
The equation of the given curve is 9y2 = x3.
Differentiating with respect to x.

the slope of the normal to the given curve at point (x1, y1)

The equation to the normal to the curve is (x1, y1)


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

Also the point (x1, y1) lies on the curve, so we have

From i and ii we have

from ii we have


Hence the points required are


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