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Find the points on the curve 9y2 = x3 where normal to the curve makes equal intercepts with the axes.
Asked by Topperlearning User | 07 Aug, 2014, 12:43: PM

Let the required point be (x1, y1)

The equation of the curve is 9y2 = x2
Since (x1, y1) lies on the curve. Therefore,

Now, 9y2 = x3

Since the normal to the curve at (x1, y1) make equal intercepts with the coordinate axes. Therefore,
Slope of the normal = ± 1

Putting x1 = 0 in (i), we get
Putting x1 = 4 in (i), we get
But, the line making equal intercepts with the coordinate axes cannot pass through the origin.
Hence, the required points are
Answered by | 07 Aug, 2014, 02:43: PM

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