Final answer:
Conic sections are defined by the general conic equation with specific parameters determining whether the shape is a circle, ellipse, parabola, or hyperbola. For parabolas in particular, with the proper parameters, we can solve for their specific forms using the quadratic formula.
Step-by-step explanation:
When dealing with conic sections, different parameters in the general conic equation Ax²+Cy²+Dx+Ey+F=0 help determine which type of conic is represented. The conics include the circle, ellipse, parabola, and hyperbola. For instance, when A=C and D=E=0, you have a circle. An ellipse arises when A and C are of the same sign but not necessarily equal, while a parabola is formed when either A or C is zero but not both. A hyperbola is characterized by A and C having opposite signs.
The general quadratic equation ax²+bx+c=0 is relevant for parabolas which can be solved using the quadratic formula. The trajectory equation y=ax+bx², given by a physics context, is another example of an equation describing a parabola where the coefficients a and b follow the physical interpretation of the context.