JEE Advanced 2013 · Paper 2 · Mathematics Q55

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MathematicsSingle correct+3 / -1Question 55 of 60

Passage

Paragraph for Questions 55 and 56

Let $PQ$ be a focal chord of the parabola $y^2=4ax$ . The tangents to the parabola at $P$ and $Q$ meet at a point lying on the line $y=2x+a$ , $a>0$ .

Length of chord $PQ$ is

7a

5a

2a

3a

Answer and worked solution

Official answer: B

Tangents at the ends of a focal chord meet on the directrix $x=-a$ ; on $y=2x+a$ that point is $(-a,-a)$ .

Parameters. The tangents at $t_1$ , $t_2$ meet at $\left(at_1t_2,\ a(t_1+t_2)\right)$ with $t_1t_2=-1$ , so $t_1+t_2=-1$ .

Length. $PQ=a(t_1-t_2)^2=a\left[(t_1+t_2)^2-4t_1t_2\right]=5a$ .

(B)

Topics:Parabola Tangents and normals to conics

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JEE Advanced 2013 · Paper 2, Mathematics question 55