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Question: The curves x<sup>2</sup> – y<sup>2</sup> = 5 and \(\frac{x^{2}}{18} + \frac{y^{2}}{8}\) = 1 cut each...

The curves x2 – y2 = 5 and x218+y28\frac{x^{2}}{18} + \frac{y^{2}}{8} = 1 cut each other at any common point at an angle

A

π4\frac{\pi}{4}

B

π3\frac{\pi}{3}

C

π2\frac{\pi}{2}

D

None of these

Answer

π2\frac{\pi}{2}

Explanation

Solution

If ax2 + by2 = 1 & a ′x2 + b1y2 = 1 cuts orthogonally then 1a−1a′=1b−1b′\frac{1}{a} - \frac{1}{a'} = \frac{1}{b} - \frac{1}{b'} ⇒ 11/5−11/18=1−5−11/8\frac{1}{1/5} - \frac{1}{1/18} = \frac{1}{- 5} - \frac{1}{1/8}

⇒ –13 = –13