Question

The differential equation of all conics whose centre lie at the origin is of order:

• A. $2$
• B. $3$
• C. $4$
• D. None of these

Answer 1

The correct option is B

$3$

Explanation for correct option

Calculating the order of the differential equation

Given, that the center of the conics lies at the origin $(0,0)$.

The general equation of all the conics with a centre at origin can be written as,

${\mathrm{\alpha x}}^2+2\mathrm{hxy}+{\mathrm{by}}^2+\mathrm{c}=0$

On dividing the above equation by $a$ we get:

${\mathrm{x}}^2+\left(\frac{2\mathrm{h}}{\mathrm{\alpha }}\right)\mathrm{xy}+\left(\frac{\mathrm{b}}{\mathrm{\alpha }}\right){\mathrm{y}}^2+\left(\frac{\mathrm{c}}{\mathrm{\alpha }}\right)=0$

Since, the equation has three parameters $\frac{2\mathrm{h}}{\mathrm{\alpha }},\frac{\mathrm{b}}{\mathrm{\alpha }},\frac{\mathrm{c}}{\mathrm{\alpha }}$ , the equation is of order $3$.

Hence, Option (B) is correct.