Question

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

• A. Statement-1 is true; Statement-2 is true; Statement-2 is a correct explanation for statement-1.
• B. Statement-1 is true; Statement-2 is true; Statement-2 is not a correct explanation for statement-1.
• C. Statement-1 is true; Statement-2 is false.
• D. Statement-1 is false; Statement-2 is true.

Answer 1

Answer: (B)

Statement-1 : $y^{2}=\pm 4ax$
$\Rightarrow \quad \frac{dy}{dx} = \pm 2a. \frac{1}{y} \Rightarrow \frac{dy}{dx} \propto \frac{1}{y}$
Statement -2 : $y^{2}=\pm 4ax \quad\Rightarrow \quad2y \frac{dy}{dx} = 4a$
Thus both statements are true but statement-2 is not a correct explanation for statement-1.