Question

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

(A) (B)

(C) (D)

Answer 1

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.