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Q.

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 II : The system of parabola $y^{2} = 4 ax$ satisfies a differential equation of degree 1 and order 1

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a

$Statement 1 and statement 2 are both true$

b

$Statement 1 is false and statement 2 is true$

c

$Statement 1 and Statement 2 are both false$

d

Statement 1 is true and

statement 2 is false

answer is B.

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Detailed Solution

$P = ({at}^{2}, 2 at), slope o f \tan g e n t a t P = \frac{1}{t}$

Clearly Statement 1 is true

Statement - 2: $Given parabola y^{2} = 4 a x d i f f w . r . t o x o n b o t h s i d e s$

$\Rightarrow 2 y \frac{dy}{dx} = 4 a \Rightarrow 2 y \frac{dy}{dx} = \frac{y^{2}}{x} \Rightarrow \frac{dy}{dx} = \frac{y}{dx}$

Degree 1, order 1

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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 PStatement II : The system of parabola y2=4ax satisfies a differential equation of degree 1 and order 1