If the line touches the hyperbola

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

Problem

If the line 2x+6y=22x + \sqrt{6}y = 2 touches the hyperbola x2−2y2=4x^2 - 2y^2 = 4 , then the point of contact is (1) (−2,6)(-2, \sqrt{6}) (2) (−5,26)(-5, 2\sqrt{6}) (3) (12,16)\left(\frac{1}{2}, \frac{1}{\sqrt{6}}\right) (4) (4,−6)(4, -\sqrt{6})

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