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# What is the relation between $b$ and $a$ for an hyperbola?

$\begin{array}{1 1}(a)\;e=\sqrt{1+\big(\large\frac{b}{a}\big)}\\(b)\;e=\sqrt{1+\big(\large\frac{a^2}{b^2}\big)}\\(c)\;e=\sqrt{1-\big(\large\frac{b^2}{a^2}\big)}\\(d)\;e=\sqrt{1+\big(\large\frac{b^2}{a^2}\big)}\end{array}$

The relation between $b$ and $a$ for an hyperbola is $e=\sqrt{1+\big(\large\frac{b^2}{a^2}\big)}$
Hence (d) is the correct answer.