Ellipse
We can stretch a circle horizontally and vertically by different factors.
Example: centre at (0, 0), horizontal stretch of 3, vertical stretch of 8
Equation:
Sketch:
TF:
SF:
GF:
Mapping Notation:
An ellipse has two axes: a major axis and a minor axis.
The major axis is the longer of the two axes. For the
previous equation
The vertical axis is the major axis
and it is 2 x 8 = 16 units long.
The horizontal axis is the minor
axis and 2 x 3 = 6 units long.
Ellipse Equations
Example 1:
We will only focus on 1 form of the equation.
The equation an ellipse is given by
Transformational Form:
NOTICE: The denominators are different.
Standard Form:
General Form:
center =
major axis =
minor axis =
(x,y)
sketch a graph
MAJOR AXIS: 2a or 2b (whichever is larger)
MINOR AXIS: 2a or 2b (whichever is smaller)
Example 2:
Example 3:
The equation an ellipse is given by
The equation an ellipse is given by
center =
center =
major axis =
major axis =
minor axis =
minor axis =
(x,y)
(x,y)
sketch a graph
sketch a graph
Example 4:
Example 5
The equation an ellipse is given by
Determine the centre and the lengths of the major and minor axis.
Then, write the equation of the ellipse in transformational form.
center =
major axis =
minor axis =
(x,y)
sketch a graph
Example 6
Determine the centre and the lengths of the major and minor axis.
Then, write the equation of the ellipse in transformational form.