Copy of Ellipse (Graph & Equation Anatomy)
Move the various sliders in this applet around to investigate what happens to the graph of an ellipse as you change various parameters within the standard form of its equation.
For example moving the blue dot on the left hand side changes something in the graph as well as the equation. Make note of those changes.
Do that for each slider so you can investigate the various parameters (a, b, h, k) observed in the graph and the equation.
Key questions to ponder as you explore:
Is it ever possible for the graph of an ellipse to become a circle? If so, under what condition(s) will this happen?
Is it possible to tell the location of an ellipse's center just by looking at its equation? If so, how?
How can the length of an ellipse's semimajor & semiminor axes be determined just by looking at its equation?
What must happen to ensure that the graph's major axis is horizontal? Vertical?
What must happen to ensure that the graph's minor axis is horizontal? Vertical?
Questions are located above the applet.
1. Is it possible to tell the location of an ellipse's center just by looking at its equation? If so, how?
2. How can the length of an ellipse's semimajor (half of the length of the major axis) & semiminor (half of the length of the minor axis) minor axes be determined just by looking at its equation?
What must happen to ensure that the graph's major axis is horizontal? Vertical?
What must happen to ensure that the graph's minor axis is horizontal? Vertical?
What must happen if we want the graph to be a circle instead of an ellipse?