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JEE Advanced 2011Paper 2
Exam
JEE Advanced
Year
2011
Paper
Paper 2
Subject
Mathematics
Chapter
Parabola

JEE Advanced 2011 · Paper 2 · Mathematics · Parabola

Let L be a normal to the parabola y^2=4 x . If L passes through the...

Let LL be a normal to the parabola y2=4xy^2=4 x. If LL passes through the point (9,6)(9,6), then LL is given by

Options

  1. Ay−x+3=0y-x+3=0
  2. By+3x−33=0y+3 x-33=0
  3. Cy+x−15=0y+x-15=0
  4. Dy−2x+12=0y-2 x+12=0

Correct answer

A. y−x+3=0y-x+3=0

Step-by-step solution

Normal to y2=4xy^2=4 x, is y−mx−2m−m3y-m x-2 m-m^3 which passes through (9,6)(9,6). Now, 6=9m−2m−m3\quad 6=9 m-2 m-m^3 ⇒m3−7m+6=0⇒m=1,2,−3\Rightarrow m^3-7 m+6=0 \Rightarrow m=1,2,-3 ∴\therefore Equation of normals are y−x+3=0y-x+3=0 y+3x−33=0y+3 x-33=0 and y−2x+12=0y-2 x+12=0
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