A Little About Parametrics for Conics

Ellipses

We know that the standard form for this conic section is (x^2)/a +(y^2)/b = 1

The parametric equation for an ellipse is x = a * cos (t)
y = b * sin (t)

Hyberbolas

We know that the standard form for this conic section is (x^2)/a - (y^2)/b = 1

The parametric equation for an hyperbola is

y = a * sec (t)

x = b * tan (t)

*the y values and x values will vary according to what axis the hyperbola is on

Parabola

The parametric equation for the parabola is

x = t^2/4p

y = t

The standard equation for the parabola is x^2 = 4py and y^2 = 4px

* Make sure to set the mode of the TI-89 to Parametric