Tangents are drawn to the hyperbola

MATHEMATICS · Single correct · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

Tangents are drawn to the hyperbola x29−y24=1\frac{x^2}{9} - \frac{y^2}{4} = 1 , parallel to the straight line 2x−y=12x - y = 1 . The points of contact of the tangents on the hyperbola are (1) (922,12)\left( \frac{9}{2\sqrt{2}}, \frac{1}{\sqrt{2}} \right) (2) (−922,−12)\left( -\frac{9}{2\sqrt{2}}, -\frac{1}{\sqrt{2}} \right) (3) (33,−22)(3\sqrt{3}, -2\sqrt{2}) (4) (−33,22)(-3\sqrt{3}, 2\sqrt{2})

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