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JEE Advanced 2013Paper 2
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 PQP Q be a focal chord of the parabola y2=4axy^{2}=4 a x. The tangents to the parabola at PP and QQ meet at a point lying on the line y=2x+a,a>0y=2 x+a, a>0.
Question: Length of chord PQP Q isParagraph: 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

Options

  1. A7a7a
  2. B5a5a
  3. C2a2a
  4. D3a3a

Correct answer

B. 5a5a

Step-by-step solution

R lies on y = 2x + a
R,y=2x+aR, y = 2x + a
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
⇒a(t−1t)=−a⇒ \text{a} \left(\text{t} - \dfrac{1}{\text{t}}\right) = - \text{a}
t−1t=−1\text{t} - \dfrac{1}{\text{t}} = - 1
⇒(t+1t)2=1+4=5⇒ {\left(\text{t} + \dfrac{1}{\text{t}}\right)}^{2} = 1 + 4 = 5
PQ=a(t+1t)2=5a\text{PQ} = \text{a} {\left(\text{t} + \dfrac{1}{\text{t}}\right)}^{2} = 5 \text{a}
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