This interactive graph illustrates the key components of a parabola based on the equation $x^2 = 4ay$. You can adjust the parameter 'a' using the slider below the graph.
- Vertex: The turning point of the parabola, located at $(0,0)$.
- Focus: A fixed point $(0, a)$ that defines the parabola. All points on the parabola are equidistant from the focus and the directrix.
- Directrix: A fixed line $y = -a$ that defines the parabola.
- Axis of Parabola: The line passing through the focus and perpendicular to the directrix, which is the line of symmetry for the parabola ($x=0$).
- Latus Rectum: A focal chord perpendicular to the axis of the parabola. Its endpoints are $(\pm 2a, a)$.
- Focal Chord: Any chord of the parabola that passes through the focus.
The graph automatically adjusts to fit the screen size, ensuring a clear view of all elements.