# The slope of a curve at any point is the reciprocal of twice of the ordinate at the point and it passes through the point (4,3). The equation of the curve is - Option 1) $x^{2}=y+5$ Option 2) $y^{2}=x-5$ Option 3) $y^{2}=x+5$ Option 4) $x^{2}=y-5$

use the concept

Solution of Differential Equation -

$\frac{\mathrm{d}y }{\mathrm{d} x} =f\left ( ax+by+c \right )$

put

$Z =ax+by+c$

- wherein

Equation with convert to

$\int \frac{dz}{bf\left ( z \right )+a} =x+c$

$\frac{dy}{dx}=\frac{1}{2y}\:(given)$

$\int 2ydy=\int dx$

$\frac{2y^{2}}{2}=x+C$

$y^{2}=x+C$

$9=4+C$

$\therefore C=5$

$y^{2}-5=x$

$y^{2}=x+5$

Option 1)

$x^{2}=y+5$

Option is incorrect

Option 2)

$y^{2}=x-5$

Option is incorrect

Option 3)

$y^{2}=x+5$

Option is correct

Option 4)

$x^{2}=y-5$

Option is incorrect

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