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  4. For any curve C (which is not a straight line), the distance of tangent at any point P on the curve C from origin, is equal to ordinate of point P. The curve passes through (1,1). Minimum distance of the point (0,5) from the curve C, is

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Q. For any curve $C$ (which is not a straight line), the distance of tangent at any point $P$ on the curve $C$ from origin, is equal to ordinate of point $P$. The curve passes through $(1,1)$.
Minimum distance of the point $(0,5)$ from the curve C, is

Differential Equations

Solution:

image
$ \frac{ dy }{ dx }=\left(\frac{2 xy }{ x ^2- y ^2}\right)$
$\therefore$ On solving we get
$x^2+(y-1)^2=1 .$