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The angle between the curves $\large\frac{x^{2}}{25}+\frac{y^{2}}{9}=$$1$ and $\large\frac{x^{2}}{8}-\frac{y^{2}}{8}=$$1$ is

\[\begin{array}{1 1}(1)\frac{\pi}{4}&(2)\frac{\pi}{3}\\(3)\frac{\pi}{6}&(4)\frac{\pi}{2}\end{array}\]

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$\large\frac{x^2}{25} +\frac{y^2}{9} $$=1$-----(1)
$\large\frac{x^2}{8} -\frac{y^1}{8} $$=1$-----(2)
$\large\frac{x^2}{8} + \frac{y^2}{8} $$=1$
$a= \large\frac{1}{25} $
$b= \large\frac{1}{9} $
$A= \large\frac{1}{8} $
$B= \large\frac{-1}{8} $
$\large\frac{1}{a} -\frac{1}{b}= \frac{1}{1/25}-\frac{1}{1/9}$$=25-9=16$------(3)
$\large\frac{1}{A}-\frac{1}{B}=\large\frac{1}{1/8} = \frac{1}{1/-8}$$=8+8=16$------(4)
From (3) and (4) the given two curves intersect orthogonality
$=> \large\frac{\pi}{2}$
Hence 4 is the correct answer.
answered May 19, 2014 by meena.p

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