Fermi · Concept Library · Courses · Books · Problems · Simulations · Math Wiki · High School Fermi › Problems The equation to the common tangents to the two hyperbolas and are
MATHEMATICS · Single correct · CBSE · Mathematics · Conic Sections · Conic Sections
Problem The equation to the common tangents to the two hyperbolas x 2 a 2 − y 2 b 2 = 1 \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 a 2 x 2 − b 2 y 2 = 1 y 2 a 2 − x 2 b 2 = 1 \frac{y^2}{a^2} - \frac{x^2}{b^2} = 1 a 2 y 2 − b 2 x 2 = 1 y = ± x ± b 2 − a 2 y = \pm x \pm \sqrt{b^2 - a^2} y = ± x ± b 2 − a 2 y = ± x ± ( a 2 − b 2 ) y = \pm x \pm (a^2 - b^2) y = ± x ± ( a 2 − b 2 ) y = ± x ± a 2 − b 2 y = \pm x \pm \sqrt{a^2 - b^2} y = ± x ± a 2 − b 2 y = ± x ± a 2 + b 2 y = \pm x \pm \sqrt{a^2 + b^2} y = ± x ± a 2 + b 2 Browse the problem library