Use the fact that to find a parametrization of the part of the hyperbola that contains the point .
A particle following the parameterization , of the unit circle starts at and moves counterclockwise. At what values of is the particle at ? Give exact values.
The diagram shows a parabola that is symmetrical about the -axis and whose vertex is at the origin. It can be described by the parametric equations and , , where is a positive constant. The focus of the parabola is the point , and the directrix is the line with the equation .
Find a pair of parametric equations that describe the parabola whose focus is the point and whose directrix is the line . Include the parameter range.