The points on the curve 9y 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 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.