Mathematics

Problem

The equation to the common tangents to the two hyperbolas

\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1

and

\frac{y^2}{a^2} - \frac{x^2}{b^2} = 1

are (a)

y = \pm x \pm \sqrt{b^2 - a^2}

(b)

y = \pm x \pm (a^2 - b^2)

(c)

y = \pm x \pm \sqrt{a^2 - b^2}

(d)

y = \pm x \pm \sqrt{a^2 + b^2}