Q ​Find the points on the curve $9y^2=x^3$ where normal tothe curve  makes equal intercepts with the axes. 

Dear Student,
Here is the solution of your asked query:

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

Regards