CBSE Class 12-science Answered
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,
![9 straight y subscript 1 squared equals straight x subscript 1 cubed...... left parenthesis straight i right parenthesis](https://images.topperlearning.com/topper/tinymce/cache/3d0e951ddab83dfc65cf9d5578763952.png)
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
![9 straight y subscript 1 squared equals 0 rightwards double arrow straight y subscript 1 equals 0](https://images.topperlearning.com/topper/tinymce/cache/4072990b2458c888781f36d3ad3bb07c.png)
Putting x1 = 4 in (i), we get
![9 straight y subscript 1 squared equals 4 cubed rightwards double arrow straight y subscript 1 equals plus-or-minus 8 over 3](https://images.topperlearning.com/topper/tinymce/cache/b5c1f30dcc55a484b2606cf3a910898f.png)
But, the line making equal intercepts with the coordinate axes cannot pass through the origin.
Hence, the required points are ![open parentheses 4 comma 8 over 3 close parentheses space & space open parentheses 4 comma minus 8 over 3 close parentheses](https://images.topperlearning.com/topper/tinymce/cache/5a3ffca5befddcdc33699f5f81bcac37.png)
![open parentheses 4 comma 8 over 3 close parentheses space & space open parentheses 4 comma minus 8 over 3 close parentheses](https://images.topperlearning.com/topper/tinymce/cache/5a3ffca5befddcdc33699f5f81bcac37.png)
Answered by | 07 Aug, 2014, 14:43: PM
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