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The curve amongst the family of curves,...

The curve amongst the family of curves, represented by the differential equation `(x^2-y^2)dx+2xydy=0` which passes through (1,1) is

A

A circle with centre on the y-axis

B

An ellipse with major axis along the y-axis

C

A circle with centre on the x-axis

D

A hyperbola with transverse axis along the x-axis

Text Solution

Verified by Experts

The correct Answer is:
C
`(x^(2)-y^(2))dx+2xydy=0`
`(dy)/(dx)=(y^(2)-x^(2))/(2xy)`
`y=tx`
`(dy)/(dx)=t+x(dt)/(dx)`
`t+x(dt)/(dx)=(t^(2)-1)/(2t) rArr x (dt)/(dx)= (-(t^(2)+1))/(2t)`
`int (2t)/(t^(2)+1)dt = int -(dx)/(x)" In" (t^(2)+1)+"In"x=c`
`x(t^(2)+1)=c`
`x((y^(2))/(x^(2))+1)=c`
`y^(2)+x^(2)-cx=0`
`therefore ` A circle with centre on x-axis.
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