Ellipses

Question 1

Major Axis

Answer 1

Longest line and have vertices, foci, and center. Also equals 2a

Question 2

Minor Axis

Answer 2

Shorter line and have co-vertices. Also equals 2b

Question 3

Standard form of a Horizontal Ellipse at (0,0)

Answer 3

x^2/a^2 + y^2/b^2 = 1

Question 4

Standard Form of a Vertical Ellipse at (0,0)

Answer 4

x^2/b^2 + y^2/a^2 = 1

Question 5

Vertices

Answer 5

Lie at the end of the major axis and are + or - a from the center

Question 6

Co-Vertices

Answer 6

Lie at the end of the minor axis and are + or - b from the center

Question 7

Foci

Answer 7

Lie on the major axis (between center and vertex) and are + or - c from the center

Question 8

How to find a, b, or c for an ellipse

Answer 8

c^2 = a^2 + b^2

Question 9

Standard Form of a Horizontal Ellipse at (h,k)

Answer 9

(x-h)^2/a^2 + (y-k)^2/b^2 = 1

Question 10

Standard Form of a Vertical Ellipse at (h,k)

Answer 10

(x-h)^2/b^2 + (y-k)^2/a^2 = 1

Question 11

Horizontal Ellipse vs. Vertical Ellipse?

Answer 11

1. If a^2 (bigger number) is first, the ellipse is horizontal. If b^2 (smaller number) is first, the ellipse is vertical
2. A change in the x-coordinates indicate a Horizontal Ellipse (horizontal = along the x-axis)
3. A change in the y-coordinate indicates a Vertical Ellipse (vertical = along the y-axis)
4. If a^2 is under the x^2, then the ellipse is Horizontal
5. If a^2 is under the y^2
6. x^2 and y^2 don’t really matter, the placement of the a^2 and b^2 tell whether the ellipse is horizontal or vertical

Question 12

a^2 vs. b^2

Answer 12

1. a^2 is ALWAYS bigger than b^2
2. If a^2 (the larger number) is first in the equation, the ellipse is horizontal
3. If b^2 (the smaller number) is first in the equation, the ellipse is vertical

Question 13

Identifying an Ellipse from its General Form Equation

Answer 13

1. 2 squared numbers (#x^2 and #y^2)

2. The two squared numbers have the same signs (positive/are being added)