Question

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

(A) (4,+8/3)        (B)  (4,-8/3)

(C) (4,+3/8)           (D)  ( 4,+3/8)

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 (x₁, y₁) is

It is given that the normal makes equal intercepts with the axes.
Therefore, We have:

The correct answer is A.