If it is mentioned that for a curve passing through $(3,4)$, the slope of the curve at any point is the…
If it is mentioned that for a curve passing through $(3,4)$, the slope of the curve at any point is the reciprocal, of twice the ordinate of that point, then that curve is a
Ellipse
Parabola
Hyperbola
Circle
Solution
According to given information the slope of curve at point $(x, y)$ is
$
\frac{d y}{d x}=\frac{1}{2 y} \Rightarrow \int 2 y d y=\int d x
$
$
\Rightarrow \quad y^2=x+c
$
$\because$ Curve (i) passes through point $(3,4)$, so $c=13$.
$\therefore$ Required curve $y^2=x+13$ and it is a parabola