Question

The equation of the curve whose subnormal is equal to a constant $a$ is:

• A. $y=ax+b$
• B. $y^2=2ax+2b$
• C. $a{y}^2-x^3=a$
• D. none of these

Answer 1

The correct option is B $y^2=2ax+2b$

According to the given condition
$y\frac{dy}{dx}=a\Rightarrow ydy=adx$
$\Rightarrow \frac{y^2}{2}=ax+b\Rightarrow y^2=2ax+2b$