Question

The differential equation of all conics whose axes coincide with the axes of coordinates is of order

• A. 2
• B. 3
• C. 4
• D. 1

Answer 1

Answer: (A)

$P(x,y)=a{x}^2+b{y}^2+2hxy+2gx+2fy+c=0$
$ax+hy+g=0$
$\frac{dP}{dx}=0\Rightarrow 2ax+2hy+2g=0$
$by+hx+f=0$
$\frac{dP}{dy}=0\Rightarrow 2by+2hx+2f=0$
$\Rightarrow h=g=f=0$
conic : $a{x}^2+b{y}^2+c=0$
$\Rightarrow x^2+\left(\frac{b}{a}\right)y^2+\frac{c}{a}=0$ order $=2$