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10.2 parabola,ellipse,hyperbola — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS10.2 parabola,ellipse,hyperbola1 Mark
MCQ
Two tangents are drawn from a point $(- 2, - 1)$ to the curve, $y^2 = 4x.$ If $\alpha $ is the angle between them, then $\left| {\tan \,\alpha } \right|$  is equal to
  • A
    $\frac {1}{3}$
  • B
    $\frac {1}{\sqrt 3}$
  • C
    $\sqrt 3$
  • ✓
    $3$
✓

Answer

Correct option: D.
$3$
d
The locus of the point of intersection of tangents to the parabola ${y^2} = 4ax$ inclined at an angle $\alpha $ to each other is 

${\tan ^2}\alpha {\left( {x + a} \right)^2} = {y^2} - 4ax$

Given equation of Parabola

${y^2} - 4a\left\{ {a = 1} \right\}$

Point of intersection $\left( { - 2, - 1} \right)$

${\tan ^2}\alpha {\left( { - 2 + 1} \right)^2} = {\left( { - 1} \right)^2} - 4 \times 1 \times \left( { - 2} \right)$

$ \Rightarrow {\tan ^2}\alpha  = 9$

$ \Rightarrow \tan \alpha  =  \pm 3$

$ \Rightarrow \left| {\tan \alpha } \right| = 3$

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