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  • Statement 1 : The slope of the tangent at any point   on a parabola , whose axis is the axis of <img

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 propotional 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 .

Option: 1

Statement-1 is true; Statement-2 is true;

Statement-2 is a correct explanation for statement-1.


Option: 2

Statement-1 is true; Statement-2 is true;

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


Option: 3

Statement 1 is true ; Statement 2 is false .


Option: 4

Statement 1 is false  ; Statement 2 is  true .


Answers (1)

Statement 1: y^2=\pm4ax

\Rightarrow \frac{d y}{d x}=\pm 2 a \cdot \frac{1}{y} \Rightarrow \frac{d y}{d x} \propto \frac{1}{y}

Statement 2 : 

y^{2}=4 a x \Rightarrow 2 y \frac{d y}{d x}=4 a

Thus both statements are true but a statement- 2 is not a correct explanation for statement-1.

Posted by

Ramraj Saini

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