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Q)

Find the equation of hyperbola if the distance between the foic is $16, e=\sqrt 2$ and axis along x-axis with centre oxgin.

$\begin{array}{1 1}(A)\;x^2+y^2=8 \\(B)\;x^2-y^2=32 \\(C)\;x^2+y^2=1 \\(D)\;x^2+y^2=64 \end{array}$

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A)
$b^2=a^2(e^2-1)$
=> $b^2=a^2$
=> $b=a$
$2ae=16$
$a=4 \sqrt 2$
Since $e=\sqrt 2$ given
Equation of hyperbola is
$\large\frac{x^2}{32}-\frac{y^2}{32}$$=1$
or $x^2-y^2=32$
Hence B is the correct answer.
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