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  • From the point (0,1) two tangents are drawn to the hyperbola . If <im

From the point (0,1) two tangents are drawn to the hyperbola \mathrm{2 x^2-y^2=1}. If \mathrm{\theta} is the angle between them, then \mathrm{\tan \theta=}

Option: 1

\frac{4}{3}


Option: 2

\frac{3}{4}


Option: 3

\frac{3}{2}


Option: 4

\frac{2}{3}


Answers (1)

best_answer

Tangent with slope m is \mathrm{y=m x \pm \sqrt{a^2 m^2-b^2}} It passes through (0,1).

\mathrm{ \begin{aligned} & \therefore \quad 1=\sqrt{\frac{m^2}{2}-1} \text { since } a^2=\frac{1}{2}, b^2=1 \\ & \Rightarrow 1=\frac{m^2}{2}-1 \Rightarrow m= \pm 2 \Rightarrow \tan \theta=\left|\frac{2-(-2)}{1-4}\right|=\frac{4}{3} . \end{aligned} }

Posted by

Ritika Kankaria

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