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JEE Main 201412 AprilOnline
Exam
JEE Main
Year
2014
Date
12 April
Mode
Online
Subject
Mathematics
Chapter
Parabola

JEE Main 2014 · 12 April · Online · Mathematics · Parabola

Two tangents are drawn from a point (-2,-1) to the curve, y^2=4 x ....

Two tangents are drawn from a point (−2,−1)(-2,-1) to the curve, y2=4x\mathrm{y}^2=4 \mathrm{x}. If α\alpha is the angle between them, then ∣tan⁡α∣|\tan \alpha| is equal to:

Options

  1. A13\frac{1}{3}
  2. B13\frac{1}{\sqrt{3}}
  3. C3\sqrt{3}
  4. D3

Correct answer

D. 3

Step-by-step solution

The locus of the point of intersection of tangents to the parabola y2=4axy^2=4 a x inclined at an angle α\alpha to each other is tan⁡2α(x+a)2=y2−4ax\tan ^2 \alpha(x+a)^2=y^2-4 a x Given equation of Parabola y²=4 x\{a=1\} Point of intersection (−2,−1)(-2,-1) tan⁡2α(−2+1)2=(−1)2−4×1×(−2)⇒tan⁡2α=9⇒tan⁡α=±3⇒∣tan⁡α∣=3\begin{aligned} &\tan ^2 \alpha(-2+1)^2=(-1)^2-4 \times 1 \times(-2) \\ &\Rightarrow \tan ^2 \alpha=9 \\ &\Rightarrow \tan \alpha=\pm 3 \\ &\Rightarrow|\tan \alpha|=3 \end{aligned}
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