If the line touches the hyperbola at the point

MATHEMATICS · Subjective · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

If the line y=mx+a2m2−b2y = mx + \sqrt{a^2 m^2 - b^2} touches the hyperbola x2a2−y2b2=1\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 at the point (asec⁡θ,btan⁡θ)(a \sec \theta, b \tan \theta) , show that θ=sin⁡−1(bam)\theta = \sin^{-1} \left( \frac{b}{am} \right) .

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