Function defined by a relation in the form f(x) = \(\frac{b}{a}\) \(\sqrt{{a}^{2}~ – {x}^{2}}\) or f(x) = − \(\frac{b}{a}\) \(\sqrt{{a}^{2}~ – {x}^{2}}\) where a is the horizontal half-axis and b is the vertical half-axis of an ellipse centered on the origin point.
Examples
Here is a graph of a function defined by the f(x) = \(\dfrac{1}{3}\) \(\sqrt{{9}~ – {x}^{2}}\) :
Here is a graph of the function defined by the relation f(x) = − \(\dfrac{1}{3}\) \(\sqrt{{9}~ – {x}^{2}}\) :
