Question

A curve is passing through the point (3, 4). At any point on that curve, its slope is equal to the reciprocal of twice the ordinate of that point. Then

• A. Equation of the curve is $x^2=y+5$
• B. Equation of the curve is $y^2=x+13$
• C. Vertex of the curve is (-13,0)
• D. Vertex of the curve is (0,-5)

Answer 1

Answer: (B), (C)

The correct options are
B Equation of the curve is $y^2=x+13$
C Vertex of the curve is (-13,0)

$\frac{dy}{dx}=\frac{1}{2y}\Rightarrow 2ydy=dx$
$\Rightarrow y^2=x+c$
It P.T (3, 4) $\Rightarrow$ c=13
$\therefore$ eqn of curve is $y^2=x+13,$
Which is a parabola, vertex is (-13, 0)