The general equation of a conic
can tell you the kind of conic it defines even when
. The following rule applies:
Let
, then the equation defines
an ellipse if
.
a parabola if
.
a hyperbola if
.
Tell what kind of conic each equation represents. On your
own graph paper, graph each function by solving for
. (
Hint: To do this, you may need the quadratic formula, regarding
as the variable and
as part of the coeffiecient of
.
(a) Conic: hyperbola
y= ________________
(b) Conic: ellipse
y= ________________
(c) Conic: parabola
y= ________________