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Question

If the curve passing through P(4,2), satisfying the differential equation dydx=yxy2 is a conic, then which of the following statements is (are) correct?

A
Focus of the conic lies on line y=2.
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B
Equation of directrix of conic is 4x17=0.
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C
Eccentricity of the conic is 1.
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D
Eccentricity of the conic is 3.
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Solution

The correct option is C Eccentricity of the conic is 1.
dxdy=xyy
dxdy1yx=y
IF=e1ydy=1y
x1y=1yy dy+c
x1y=y+c
x=y2+cy
As the curve passes through (4,2), we get c=4
Hence, the curve is x=y2+4y
(x4)=(y2)2
(y2)2=(x4).
Eccentricity of parabola is always 1


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