The curve is such that the length of the perpendicular from the origin on the tangent at any point `P` of the curve is equal to the abscissa of`Pdot` Prove that the differential equation of the curve is`y^2-2x y(dy)/(dx)-x^2=0,` and hence find the curve.

Explanation

The tangent at` P(x, y)` is
`

Y-y=((dy) / (dx))(X-x)`


If p be the length of perpendicular from the origin, then


`p=|frac{x frac{d y}{d x}-y}{sqrt{1+(frac{d y}{d x})^{2}}}|`


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