1.

The equation of the curve whose slope is given by `(dy)/(dx)=(2y)/x ; x >0, y >0`and which passes through the point (1,1) is`x^2=y`b. `y^2=x`c. `x^2=2y`d. `y^2=2x`A. CircleB. ParabolaC. EllipseD. hyperbola

Answer» Correct Answer - B
`(dy)/(dx)=(2y)/x`
`implies (dy)/y=2 (dx)/x`
On integration
`int (dy)/y=2 int (dx)/x`
`implies log y=2 log x+log a`
`implies log y=log x^(2)+log a`
`implies log y=log (a^(2).a)`
`implies y=x^(2)a`
at `(1, 1), a=1`
`implies x^(2)=y=4 (1/4) y`
`implies` the curve is parabola.


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