Parabolas Page 1

Page 1

Varying the Coefficients in the General Equation
to find Parabolas that Open Up or Down

In our study of conic sections we have learned that:
if the equation Ax² + By²+ Cx + Dy + F = 0 defines a circle, then the coefficients of x² and y² must be equal, that is A = B.
if the equation Ax² + By² + Cx + Dy + F = 0 defines an ellipse that is not a circle, then the coefficients of x² and y² must be different, that is A B.
if the equation Ax² + By² + Cx + dy + F = 0 defines a hyperbola, then the product of the coefficients of x² and y² must be less than zero, that is AB < 0.

What would happen if either A = 0 or B = 0 in the equation Ax² + By² + Cx + Dy + F = 0?

Use the action figure to explore the case when B = 0. Once you've come to some conclusions, answer the questions in the question box.

Ax² + ~~By²~~ + Cx + Dy + F = 0