If the relation between subnormal SN and subtangent ST at any point on the curve $by^2=(x+a)^2$ is $p(SN)=q(ST)^2$, then p/q =
Answer & explanation
Correct answer: option 3
$by^2=(x+a)^2⇒\frac{dy}{dx}=\frac{3(x+a)^2}{2by}$
Subnormal (S.N.) = $y.\frac{3(x+a)^2}{2by}=\frac{3}{2b}(x+a)^2$ and
Subtangent (S.T.) = $y.\frac{2by}{3(x+a)^2}=\frac{2.(x+a)^3}{3(x+a)^2}=\frac{2}{3}(x+a)$
$\frac{p}{q}=\frac{(S.T.)^2}{S.N}=\frac{\frac{4}{9}(x+a)^2}{\frac{3}{2b}(x+a)^2}=\frac{8b}{27}$