Q Find the points on the curve 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