Question

What is General Conic Form?

Answer 1

General Conic Form

• A conic includes shapes like a circle, parabola, ellipse, and hyperbola.
• Each shape is formed when a cone is cut by a plane at different angles.
• The general form of a conic is $A{x}^2+Bxy+C{y}^2+Dx+Ey+F=0$ where $A,B,C,D,E,F$are constants.
• The difference in the equation of conics depends upon the values of $A,C$

1. For circles, the values of $A,C$ are equal in magnitude and sign i.e.,$\begin{array}{r}A=C\end{array}$
2. For ellipses, the values of $A,C$ have the same sign and different values i.e,$\begin{array}{r}A,C>0,A\ne C\end{array}$
3. For hyperbolas, the values of $A,C$ have opposite signs i.e., $\begin{array}{r}C<0<A\end{array}$ or $\begin{array}{r}A<0<C\end{array}$
4. For parabolas, either of the values of $A,C$ must be zeroi.e.,$\begin{array}{r}A=0\end{array}$ or $C=0$