# 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 ellipse is

$\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\:\:\:but\ 1-\frac{b^{2}}{a^{2}}=\frac{3}{4}$

$\therefore \frac{x^{2}}{4b^{2}}+\frac{y^{2}}{b^{2}}=1\:\:\:\therefore \frac{b^{2}}{a^{2}}=\frac{1}{4}$

$\therefore x^{2}+4y^{2}=4b^{2}\:\:\:\therefore a^{2}=4b^{2}$

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

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

$order=1\\ degree=1$

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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