The equation above is the standard form equation of a horizontal parabola and have the next caractheristics:
- The vertex is (h,k)
- If 4p > 0, it opens right
If 4p < 0, it opens left
- | p | is the distance from the vertex to the focus
- The directrix is vertical and the vertex is midway betweeen the focus and directrix
- The directrix is 2| p | units from the focus
For the given parabola:
Focus coordinates: It has the same y-coordinate that the vertex, the x-coorcdinate is |p| units to the right (as the parabola opens right) from the x-coordinate of the vertex:
Directrix: it is a vertical line as follow (for a parabola that opens right)
The vertex of the parabola is (3, -1). The parabola opens right, and the focus is 3 units away from the vertex. The directrix is 6 units from the focus. The focus is the point (6, -1). The directrix of the equation is x=0