﻿ Find the abscissa of the point on the curve ay2 = x3, the normal at which cuts of equal intercept from the axes. : Kaysons Education

# Find The Abscissa Of The Point On The Curve ay2 = x3, The Normal At Which Cuts Of Equal Intercept From The Axes.

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## Question

### Solution

Correct option is

x = 4a/9

The given curve is ay2 = x3                    …(i)

Differentiate to get:

The slope of normal

Since the normal makes equal intercepts on the axes its inclinations to axis of x is either 45o or 135o.

So two normal are possible with slopes 1 and –1.

One squaring 4a2y2 = 9x4. Using (i) we get:

4a x3 = 9x4        ⇒     x = 4a/9.

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