The sub-normal at any point of the curve x2y2=a2x2−a2 v
![The sub-normal at any point of the curve x2y2=a2x2−a2 v](/img/relate-questions.png)
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The sub-normal at any point of the curve x2y2=a2(x2−a2) varies as
A.
(Abcissa)−3
B.
(Abcissa)3
C. (Ordinate)−3
D. (Ordinate)3
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Right Answer is: A
SOLUTION
We have, x2 y2=a2(x2−a2)...(1)⇒x2.2ydydx+y2.2x−a2.2x⇒dydx=a2−y2xy.∴Sub−normal =ydydx=a2−y2xy=x2(a2−y2)x3=a4x3[∵from (1)x2(a2−y2)=a4]
The sub-normal varies inversely as the cube of its abcissa.
Hence (a) is the correct answer.