Explanation:
(B) : Given, the center of the conic lies at the origin \((0,0)\)
The equation of all conic
\(a x^{2}+b y^{2}+2 h x y+2 g x+2 f y+C=0\)
Center lies of origin \((-g,-f)=(0,0)\) the equation \(\mathrm{ax}^{2}+2 \mathrm{hxy}+\mathrm{by}^{2}+\mathrm{C}=0\)
Dividing by a in the above equation, we get-
\(x^{2}+\frac{2 h}{a} x y+\frac{b}{a} y^{2}+\frac{c}{a}=0\)
Since, the equation has three parameters
\(\frac{2 \mathrm{~h}}{\mathrm{a}}, \frac{\mathrm{b}}{\mathrm{a}}, \frac{\mathrm{c}}{\mathrm{a}}\)
Hence, order of equation is 3