How to Identify Quadratic Equations

The standard form of a quadratic equation is: ax² + bx + cy ² + dy + e = 0

If a is equal to c in the above equation then the equation will make a circle. 2x ² + 2y² = 24; a = c so the when graphed it would be a circle.

 

If in the equation a dose NOT equal c the the equation is one for an elipse.

-4x² + -25y² = 205, because a dose not equal c but they have the same sign the equation is one of an elipse.

If a or c equals zero then the equation belongs to a parabola.

4x + 2y² = 61 in this equation a = zero so the equation is a parabola.

if a and c have different signsthen the equation is one of a hyperbola. -3x² + 3y² = 36: a and c have different signs so the the shape ia a hyperbola.