# The order and the degree of the differential equation of all ellipses with centre at the origin,major axis along x-axis and eccentricity    are, respectively : Option 1) 2,  2 Option 2) 1,  1 Option 3) 2,  1 Option 4) 1,  2

As we learnt in

Order of a Differential Equation -

The order of a differential equation is order of highest order occuring in differential equation

- wherein

order of

$\frac{d^{2}y} {dx^{2}}+5=0$

is 2.

Let the equation of ellipses is  $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$  and $1-\frac{b^{2}}{a^{2}}=\frac{3}{4}$

$\\ \therefore \frac{b^{2}}{a^{2}}=\frac{1}{4}\, \, \, \, \, \therefore a^{2}=4b^{2}$

$\\ \Rightarrow \frac{x^{2}}{4b^{2}}+\frac{y^{2}}{b^{2}}=1$

$\\ \Rightarrow x^{2}+{4y^{2}}=4b^{2}$

$\\ \Rightarrow 2x+{8y.\frac{dy}{dx}}=0$

$\therefore x+4y.\frac{dy}{dx}=0$

Order (O) $\rightarrow$ 1

Degree (D) $\rightarrow$ 1

Option 1)

2,  2

This option is incorrect.

Option 2)

1,  1

This option is correct.

Option 3)

2,  1

This option is incorrect.

Option 4)

1,  2

This option is incorrect.

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