Question

The slope of a curve at any point is the reciprocal of twice the ordinate at the point and it passes through the point $(4,3)$. The equation of the curve is

• A. $x^2=y+5$
• B. $y^2=x-5$
• C. $y^2=x+5$
• D. $x^2=y-5$

Answer 1

Answer: (C)

$y^2=x+5$

According to the question, we have

$\frac{dy}{dx}=\frac{1}{2y}$
$\Rightarrow 2ydy=dx$
On integrating, we get
$y^2=x+C$
This passes through $(4,3)$
Therefore, $9=4+C\Rightarrow C=5$
Hence,, the equation of the curve is $y^2=x+5$.