Question

The slope of tangent of a curve, passing through $(3,4)$ at any point is the reciprocal of twice the ordinate of the point. Then the curve also passes through:

• A. $(-4,3)$
• B. $(-4,-3)$
• C. $(12,5)$
• D. $(12,-5)$

Answer 1

Answer: (A), (B), (C), (D)

$(12,-5)$

It is given that $\frac{dy}{dx}=\frac{1}{2y}.$
$\Rightarrow 2ydy=dx$
Integrating both sides, 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 clearly a parabola that passes through all given options(points).