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The slope of a curve, passing through (3...

The slope of a curve, passing through (3,4) at any point is the reciprocal of twice the ordinate of that point. Show that it is parabola.

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It is given that `(dy)/(dx) = 1/(2y)`
`2ydy=dx`
Integrating, we get `y^(2)=x+c`
Now when `x=3, y=4` which gives `c=13`
Hence the equation of the required curve is `y^(2)=x+13`, which is a parabola.
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