Question: If 4x2 + py2 = 45 and x2 – 4y2 = 5 cut orthogonal, then ...

Question

If 4x² + py² = 45 and x² – 4y² = 5 cut orthogonal, then the value of p is

Answer 1

Slope of 1st curve $\left( \frac{dy}{dx} \right)_{I} = - \frac{4x}{py}$

Slope of 2nd $\left( \frac{dy}{dx} \right)_{II} = \frac{x}{4y}$

For orthogonal intersection $\left( - \frac{4x}{py} \right)\left( \frac{x}{4y} \right)$ = -1

⇒ x² = py²

On solving equations of given curves x = 3, y = 1

∴ p(1) = (3)² = 9 ⇒ p = 9.

Question: If 4x<sup>2</sup> + py<sup>2</sup> = 45 and x<sup>2</sup> – 4y<sup>2</sup> = 5 cut orthogonal, then ...