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Question

Determine the differential equation of parabolas with foci at origin and axes along X-axis.
Hint:y2=4a(x−a)

A
y3(dydx)2=2xydydx1
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B
y4(dydx)2=2xydydx1
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C
y3(dydx)2=2xydydx2
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D
y4(dydx)3=2xydydx1
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Solution

The correct option is B y4(dydx)2=2xydydx1

Consider the equitation of parabolas with foci at origin and axes along xaxis.

y2=4a(xa) …….(1)

Differentiate with respect to x,we get


2ydydx=4a(10)

a=12ydydx


Put this value in equation 1st, we get


y2=4×12ydydx⎜ ⎜ ⎜x12ydydx⎟ ⎟ ⎟

ydydxy2=2⎜ ⎜ ⎜x12ydydx⎟ ⎟ ⎟

y3dydx=2⎜ ⎜ ⎜2xydydx12ydydx⎟ ⎟ ⎟

y4(dydx)2=2xydydx1


Hence ,this is the answer .


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