Exam

JEE Advanced

Year

2013

Paper

Paper 2

Subject

Mathematics

Chapter

Parabola

JEE Advanced 2013 · Paper 2 · Mathematics · Parabola

Paragraph: Let P Q be a focal chord of the parabola y^ 2 =4 a x ....

Paragraph: Let $P Q$ be a focal chord of the parabola $y^{2}=4 a x$. The tangents to the parabola at $P$ and $Q$ meet at a point lying on the line $y=2 x+a, a>0$.
Question: If chord $P Q$ subtends an angle $\theta$ at the vertex of $y^{2}=4 a x$, then $\tan \theta=$

Step-by-step solution

$\text{t} - \dfrac{1}{\text{t}} = - 1$
$⇒ \text{t} + \dfrac{1}{\text{t}} = \sqrt{5}$
\text\tan \theta = \dfrac{\dfrac{2}{\text{t}} + 2 \text{t}}{1 - 4} = \dfrac{2 \left(\dfrac{1}{\text{t}} + \text{t}\right)}{- 3} = \dfrac{2 \sqrt{5}}{- 3}