MAT136H1 Lecture Notes - Polar Coordinate System
10.5 Parametric Equations & Polar Coordinates
Question #1 (Easy): Vertex, Focus, Directrix for Parabola
For a parabola equation , or the focus is at or and the directrix is
or , respectively. The focus can shift horizontal and vertically in the opposite direction of
the numeric values added unto and .
Find the vertex, focus, and directrix of the parabola and sketch the graph.
The equation can be re-written in the form of ,
which means the vertex is at and since the parabola is in the form
of , , . Then the directrix is , which
means 3 units down from the vertex. Thus because of the shift of the
vertex, the directrix becomes . The focus is directly above
the vertex, but moved in the opposite direction, that is in this case
northward by the same unit that directrix is below the vertex. Thus, the
focus is at