The points on the curve 9y 2 = x 3, where the normal to the curve makes equal intercepts with the axes are
The equation of the given curve is 9y2 = x3.
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.