Question

If the curves y² = 6x, 9x² + by² = 16, cut each other at right angles then the value of b is –

• A. 2
• B. 4
• C. 9/2
• D. None of these

Answer 1

Answer: (C)

9/2

Answer 2

The intersection of the two curves is given by

9x² + 6bx – 16 = 0 (i)

Differentiating y² = 6x, we have $\frac{dy}{dx}$= $\frac{3}{y}$.

Differentiating 9x² + by² = 16, we have $\frac{dy}{dx}$ = –$\frac{9x}{by}$.

For curves to intersect at right angles, we must have at the points of intersection $\frac{3}{y}\left( \frac{- 9x}{by} \right)$ = –1 Ž 27x = by². Thus we must have

9x² + by² = 16 Ž 9x² + 27x – 16 = 0 (ii)

(i) and (ii) must be identical so 27 = 6b Ž b = 9/2.