Question

The order and the degrees of the differential equation of all ellipses with centre at the origin, major axis along $x$-axis and eccentricity $\frac{\sqrt{3}}{2}$ are, respectively:

• A. $1,1$
• B. $2,1$
• C. $1,2$
• D. $2,2$

Answer 1

Answer: (A)

$1,1$

Given, eccentricity $=e=\frac{\sqrt{3}}{2}$

We know $b^2=a^2(1-e^2)=a^2(1-\frac{3}{4})=\frac{a^2}{4}$

Equation of ellipse $=\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

Thus $\frac{x^2}{a^2}+\frac{y^2}{a^2/4}=1$

$\Rightarrow x^2+4y^2=a^2$

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

Therefore, order is $1$, degree is $1$.