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Question

The orthogonal trajectory of y2= 4ax is.

A
x2+y2 =k
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B
2x2+y2 =k
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C
x2y2 =k
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D
x3+y3 =k
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Solution

The correct option is B 2x2+y2 =k
y2 =4axDifferentiating once to form DE.2ydydx=4aEliminating arbitary constant:y2 =2ydydxxdydx=y2xSo, DE of orthogonal trajectory dydx=−2xySeparating variables2xdx + ydy=0Integrating to get the orthogonal trajectory : x2 + y22= c2x2 + y2 =2cEquating 2c to another constant k2x2 + y2 =k.This is the orthogonal trajectory.

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