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JEE Main 20139 AprilOnline
Exam
JEE Main
Year
2013
Date
9 April
Mode
Online
Subject
Mathematics
Chapter
Parabola

JEE Main 2013 · 9 April · Online · Mathematics · Parabola

Statement-1: The slope of the tangent at any point P on a parabola,...

Statement-1: The slope of the tangent at any point P\mathrm{P} on a parabola, whose axis is the axis of xx and vertex is at the origin, is inversely proportional to the ordinate of the point P\mathrm{P}. Statement-2: The system of parabolas y2=4axy^2=4 a x satisfies a differential equation of degree 1 and order 1.

Options

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

Correct answer

B. Statement-1 is true; Statement-2 is true; Statement- 2 is not a correct explanation for statement-1.

Step-by-step solution

- Statement −1:y2=±4ax⇒dydx=±-1: y^2=\pm 4 a x ⇒ \frac{d y}{d x}=\pm2 a ⋅1y⇒dydx∝1y\cdot \frac{1}{y} \Rightarrow \frac{d y}{d x} \propto \frac{1}{y}Statement −2:y2=4ax⇒2ydydx=4a-2: y^2=4 a x \Rightarrow 2 y \frac{d y}{d x}=4 a Thus both statements are true but statement-2 is not a correct explanation for statement-1.
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