Editing Parabola (section)

=== Position of the focus ===
In the diagram above, the point&nbsp;V is the [[Perpendicular#Foot of a perpendicular|foot of the perpendicular]] from the vertex of the parabola to the axis of the cone. ''The point&nbsp;F is the foot of the perpendicular from the point&nbsp;V to the plane of the parabola.''{{efn|The point&nbsp;V is the centre of the smaller circular cross-section of the cone. The point&nbsp;F is in the (pink) plane of the parabola, and the line {{overline|VF}} is perpendicular to the plane of the parabola.}} By symmetry, F is on the axis of symmetry of the parabola. Angle VPF is [[Complementary angles|complementary]] to {{mvar|θ}}, and angle PVF is complementary to angle VPF, therefore angle PVF is {{mvar|θ}}. Since the length of {{overline|PV}} is {{mvar|r}}, the distance of F from the vertex of the parabola is {{math|''r'' sin ''θ''}}. It is shown above that this distance equals the focal length of the parabola, which is the distance from the vertex to the focus. The focus and the point&nbsp;F are therefore equally distant from the vertex, along the same line, which implies that they are the same point. Therefore, ''the point&nbsp;F, defined above, is the focus of the parabola''.

This discussion started from the definition of a parabola as a conic section, but it has now led to a description as a graph of a quadratic function. This shows that these two descriptions are equivalent. They both define curves of exactly the same shape.