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Question

If the length of the subnormal of a curve is constant and if it passes through the origin, then the equation of curve is

A
x2+y2=k2;kϵR
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B
y2=kx;kϵR
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C
x2=ky2;kϵR
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D
x2y2=k2;kϵR
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Solution

The correct option is A y2=kx;kϵR
Length of the subnormal of the curve is given by ydydx
Let k1 be the constant length of the subnormal
ydydx=k1
On integrating on both the sides we get,
ydy=k1dx
y22=k1x+c
As it is passes through origin so, x=0,y=0
c=0
y2=2k1x
here 2k1=k
y2=kx,kϵR.

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