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  • Two tangents are drawn from the point to the parabola <img alt="\mathrm{y^2=4 x}" s

Two tangents are drawn from the point \mathrm{(-2,-1)} to the parabola \mathrm{y^2=4 x}. If \mathrm{\alpha} is the angle between these tangents, then

\mathrm{\tan \alpha=}
 

Option: 1

3


Option: 2

\frac{1}{3}


Option: 3

2


Option: 4

\frac{1}{2}


Answers (1)

best_answer

Equation of pair of tangent from \mathrm{(-2,-1)} to the parabola is given by \mathrm{S S_1=T^2} i.e.

\mathrm{ \begin{aligned} & \left(y^2-4 x\right)(1+8)=[y(-1)-2(x-2)]^2 \\\\ & \Rightarrow 9 y^2-36 x=[-y-2 x+4]^2 \Rightarrow 9 y^2-36 x=y^2+4 x^2+16+4 x y-16 x-8 y \Rightarrow \\\\ & 4 x^2-8 y^2+4 x y+20 x-8 y+16=0 \\\\ & \quad \tan \alpha=\left|\frac{2 \sqrt{h^2-a b}}{a+b}\right|=\left|\frac{2 \sqrt{4-4(-8)}}{4-8}\right|=\left|\frac{12}{-4}\right|=3 \\ & \therefore \quad \end{aligned} }

Posted by

Gautam harsolia

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