Subject:
To derive the focus of a simple parabola, where the axis of symmetry is parallel to the y-axis with the vertex is at (0,0), such as then there is a point (0,f) ? the focus, F ? such that any point P on the parabola will be equidistant from both the focus and the linea directrix, L. The linea directrix is a a line perpendicular to the axis of symmetry of the parabola (in this case parallel to the x axis) and passes through the point (0,-f). So any point P=(x,y) on the parabola will be equidistant both to (0,f) and (x,-f). FP, a line from the focus to a point on the parabola, has the same length as QP, a line drawn from that point on the parabola perpendicular to the linea directrix, intersecting at point Q.
