1. ALGEBRA II HONORS/GIFTED - ELLIPSES
12/9/2018
ALGEBRA II HONORS/GIFTED @
ELLIPSES

2. Desmos.com (again).

3. ALGEBRA II HONORS/GIFTED - ELLIPSES
12/9/2018
ELLIPSES
Standard Form
ax2 + by2 + cx + dy + e = 0
Center Radius Form
MUST be 1 for a ellipse!!!
(h, k) center rx= x-radius ry= y-radius

4. Major Axis: long axis all the way across the ellipse
Minor Axis: short axis all the way across the ellipse
Semi-major axis: half of the major axis
Semi-Minor Axis: half the minor axis
X-radius: the distance from the center to the ellipse in the x-direction
Y-radius: the distance from the center to the ellipse in the y-direction
Minor Axis
Vertex

5. What is a Focal Radius? If a is the length of the semi-major axis
It is the distance from the center to the focus.
If a is the length of the semi-major axis
b is the length of the semi-minor axis, and
c is the focal radius, and
d1 and d2 are the distances from a
point (x , y) on an ellipse
to the two foci.
Then
d1 + d2 = 2a = the length of the major axis,
a2 = b2 + c2, from which
c2 = a2 - b2 The formula to find the focal radius!
(x,y) d1 d2 b a c

6. 1) Standard Form to Center Radius Form
ALGEBRA II HONORS/GIFTED - ELLIPSES
1) Standard Form to Center Radius Form
12/9/2018
25x2 + 9y x + 18y = 0
IMPORTANT INFORMATION
Center rx ry rf
Length of major axis
Length of minor axis

7. ALGEBRA II HONORS/GIFTED - ELLIPSES
2) Standard Form to Center Radius Form
12/9/2018
25x2 + 49y2 – 100x + 392y – 341 = 0
IMPORTANT INFORMATION
Center rx ry rf
Length of major axis
Length of minor axis

8. 3) Find the equation of the ellipse with center (2, 5), one
focus (5, 5) and
one vertex (7, 5).

9. ELLIPSES IN EVERYDAY LIFE