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JEE Main 201322 AprilOnline
Exam
JEE Main
Year
2013
Date
22 April
Mode
Online
Subject
Mathematics
Chapter
Parabola

JEE Main 2013 · 22 April · Online · Mathematics · Parabola

Statement-1: The line x-2 y=2 meets the parabola, y^2+2 x=0 only at...

Statement-1: The line x−2y=2x-2 y=2 meets the parabola, y2+2x=0y^2+2 x=0 only at the point (−2,−2)(-2,-2). Statement-2: The line y=mx−12m(m≠0)y=m x-\frac{1}{2 m}(m \neq 0) is tangent to the parabola, y2=−2xy^2=-2 x at the point (−12m2,−1m)\left(-\frac{1}{2 m^2},-\frac{1}{m}\right)

Options

  1. AStatement-1 is true; Statement- 2 is false.
  2. BStatement-1 is true; Statement-2 is true; Statement-2 is a correct explanation for statement-1.
  3. CStatement-1 is false; Statement-2 is true.
  4. DStatement-1 a true; Statement-2 is true; Statement-2 is not a correct explanation for statement-1.

Correct answer

B. Statement-1 is true; Statement-2 is true; Statement-2 is a correct explanation for statement-1.

Step-by-step solution

Both statements are true and statement-2 is the correct explanation of statement-1 ∴\therefore \quad The straight line y=mx+amy=m x+\frac{a}{m} is always a tangent to the parabola y2=4axy^2=4 a x for any value of mm. The co-ordinates of point of contact (am2,2am)\left(\frac{a}{m^2}, \frac{2 a}{m}\right)
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