Q. The equation of the curve whose subnormal is equal to a constant $a$ is
A) $y = ax + b$
B) $y^{2} = 2ax + 2b$
C) $ay^{2} - x^{3} = a$
D) None of these
Explanation
(b)
Since, length of subnormal =$a$
$\Rightarrow$ $y\ \frac{dy}{dx} = a\ \ \Rightarrow y\ dy = a\ dx$
On integrating both sides, we get
$\frac{y^{2}}{2} = ax + b$
Where $b$ is a constant of integration
$\Rightarrow$ $y^{2} = 2ax + 2b$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.