Conic Section

General expression for a conic section in the Cartesian coordinate system is defined as: The result of determines the what the figure is: If the result is smaller than 0, then we have an ellipse, unless the conic is degenerate. The ellipse is defined as: and If the result is smaller than 0 and A=C , B=0 then we have a circle. The circle is defined as: If the result is equal to 0, then we have a parabola. The parabola is defined as: and If the result is bigger than 0, then we have a hyperbola. The hyperbola is defined as: and If the result is bigger than 0 and A+C = 0, then we have a rectangular hyperbola. The rectangular hyperbola is defined as: