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


It is given that the equation of the curve is 9y2 = x3


Differentiating w.r.t. x, we get,




The slope of the normal to the given curve at point (x1,y1) is



Then, the equation of the normal to the curve at (x1,y1)is


y – y1 =






Now, it is given that the normal makes equal intercepts with the axes.


Thus, we get,




…………………….(1)


Since, the point (x1,y1)lies on the curve …………(2)


From (1) and (2), we get




Now putting the value of x1 in (2), we get





Therefore, the required points are

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