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Question

The sub-normal at any point of the curve x2y2=a2(x2a2) varies as


A

(Abcissa)3

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B

(Abcissa)3

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C
(Ordinate)3
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D
(Ordinate)3
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Solution

The correct option is A

(Abcissa)3


We have, x2 y2=a2(x2a2)...(1)x2.2ydydx+y2.2xa2.2xdydx=a2y2xy.Subnormal =ydydx=a2y2xy=x2(a2y2)x3=a4x3[from (1)x2(a2y2)=a4]
The sub-normal varies inversely as the cube of its abcissa.
Hence (a) is the correct answer.

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