Question

The points on the curve 9y² = x³ where the normal to the curve makes equal intercepts with the axis is

• A. $\left( 4,\frac{8}{3} \right)$ or $\left( 4, - \frac{8}{3} \right)$
• B. $\left( - 4,\frac{8}{3} \right)$
• C. $\left( - 4, - \frac{8}{3} \right)$
• D. None of these

Answer 1

Answer: (A)

$\left( 4,\frac{8}{3} \right)$ or $\left( 4, - \frac{8}{3} \right)$

Answer 2

9y² = x³ …..(1) Ž 18y$\frac{dy}{dx}$= 3x²

Ž $\frac{dy}{dx} = \frac{x^{2}}{6y}$

slope of normal = $\frac{- 6y}{x^{2}}$ = ±1 Ž y = $\frac{\pm x^{2}}{- 6}$

put in (1) 9(± x²/– 6)²= x³ Ž x = ± 4