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JEE Advanced 2013 Paper 2

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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

Section: Mathematics

Question : 51 of 60

Marks: +1, -0

Length of chord PQ is

Solution:

R lies on y = 2x + a
⇒ a

\left(t - \frac{1}{t}\right)

= -a
t -

\frac{1}{t}

= -1
⇒

\left(t + \frac{1}{t}\right)^2

= 1 + 4 = 5
PQ = a

\left(t + \frac{1}{t}\right)^2

= 5a

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