Question

At any point on the curve \[ by^2=(x+a)^3, \] if the length of the sub-tangent (ST) and the length of the sub-normal (SN) are such that \[ p(\text{SN})=q(\text{ST})^2, \] then \[ \frac{p}{q}= \]

• A. \(\dfrac{2b}{9}\)
• B. \(\dfrac{8b}{27}\)
• C. \(\dfrac{5b}{8}\)
• D. \(\dfrac{27}{8b}\)

Hint:

For tangent-normal problems, remember: \[ \text{Sub-tangent}=\frac{y}{dy/dx}, \qquad \text{Sub-normal}=y\frac{dy}{dx}. \] After finding \(dy/dx\), substitute directly into these formulas.

Answer 1

The Correct Option is B