CBSE Class 12-science Answered
The slope of the curve 2y2 = ax2 + b at (1, – 1) is – 1. Find a, b
Asked by Topperlearning User | 07 Aug, 2014, 08:32: AM
The equation of the curve is
2y2 = ax2 + b …(i)
Differentiating w.r.t. x, we get
![4 straight y. dy over dx equals 2 ax](https://images.topperlearning.com/topper/tinymce/cache/d17aa58e616e8c5b673af5d46df0e877.png)
![rightwards double arrow dy over dx equals fraction numerator ax over denominator 2 straight y end fraction rightwards double arrow open parentheses dy over dx close parentheses subscript left parenthesis 1 comma minus 1 right parenthesis end subscript equals minus straight a over 2](https://images.topperlearning.com/topper/tinymce/cache/07fc91bc72814dbe8cdebcf32c7a73ef.png)
It is given that the slope of the tangent at (1, –1) is –1. Therefore,
![minus straight a over 2 equals minus 1 rightwards double arrow straight a equals 2](https://images.topperlearning.com/topper/tinymce/cache/48aab8e915aeec10bffcd4fa068127fd.png)
Since the point (1, –1) lies on (i). Therefore,
2 (–1)2 = a (1)2 + b Þ a + b = 2
Putting a = 2 in a + b = 2, we obtain b = 0.
Hence a = 2 and b = 0.
Answered by | 07 Aug, 2014, 10:32: AM
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