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  • The differential equation of all parabola having their axis of symmetry coinciding with the axis of X is  Option: 1 <img alt="y\frac{d

The differential equation of all parabola having their axis of symmetry coinciding with the axis of X is

 

Option: 1

y\frac{d^{2}y}{dx^{2}}+\left ( \frac{dy}{dx} \right )^{2}=0
 


Option: 2

y\frac{d^{2}x}{dy^{2}}+\left ( \frac{dx}{dy} \right )^{2}=0

 


Option: 3

y\frac{d^{2}y}{dx^{2}}+\frac{dy}{dx}=0


Option: 4

none of these


Answers (1)

best_answer

 

Differential Equations -

An equation involving independent variable (x), dependent variable (y) and derivative of dependent variable with respect to independent variable 
\left (\frac{\mathrm{d} y}{\mathrm{d} x} \right )

- wherein

eg:

  \frac{d^{2}y}{dx^{2}}- 3\frac{dy}{dx}+5x=0

 

 

Directrics \perp to x axis, Let x=\alpha and focus on x axis Let (\beta ,0), Now (x-\beta )^{2}+y^{2}=(x-\alpha )^{2}

\beta ^{2}-2\beta x+y^{2}=\alpha ^{2}-2\alpha x

y^{2}=2(\beta -\alpha )x+\alpha ^{2}-\beta ^{2}

In general  y^{2} = mx + c   (Two arbitrary constant m and c)

2y\frac{dy}{dx}=m

2y\frac{d^{2}y}{dx^{2}}+2\left ( \frac{dy}{dx} \right )^{2}=0

 

 

Posted by

Ritika Harsh

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