Ellipse - First Level

Definition: An ellipse is the set of points satisfying: \frac{{x^2 }}{{\color{red}{a^2} }} + \frac{{y^2 }}{{\color{blue}{b^2} }} = 1 , where a and b are positive numbers. More

This ellipse is centered at (0,0)
The axes of this ellipse are the x-axis and y-axis.
If a=b, the ellipse is a circle with radius a.
This ellipse passes through the points A=(-a,0), A'=(a,0), B=(0,b) and B'=(0,-b).
Let \color{green}{c}=\sqrt{|\color{red}{a}^2-\color{blue}{b}^2|}
- If a>b the foci are F1=(-c,0) and F2(c,0) and the principle axis length is a.
- If a<b the foci are F1=(0,c) and F2(0,-c) and the principle axis length is b.

InterActivity: Directions

In the Algebra View (at left), click and leave your mouse on d to see the definition

Ellipse d: Ellipse with foci F1 and F2 and first axis' length e]@].

In the Graphics View (at right), click and drag sliders a and b to change the shape of the ellipse.

Notice that if a=b the ellipse becomes a circle.
Slide a>b and then b>a and notice that the foci F1 and F2 shift from the x-axis to the y-axis.

Ellipse[ <Focal Point>, <Focal Point>, <Principal Axis Length> ]

Ellipse[ <Focal Point>, <Focal Point>, <Segment> ]

Ellipse[ <Point>, <Point>, <Point> ]