Question

At the point $(a,a)$ on the curve $y^2=\frac{x^3}{2a-x}$ the length of the sub normal

• A. 2a
• B. a
• C. 3a
• D. None of these

Answer 1

The correct option is A 2a

$y=\sqrt{\frac{x^3}{2a-x}}$

$\frac{dy}{dx}=\frac{1}{2}\sqrt{\frac{2a-x}{x^3}}\frac{(2a-x)3x^2+x^3}{(2a-x{)}^2}$ at$(a,a)⟹\frac{dy}{dx}=2$

so, length of sub normal$=2a$