Ellipses :D

In class this week we learned about conic sections. I will tell you about Ellipses. The standard form for an Ellipse is x^2/a^2 + y^2/b^2 = 1. To put in standard form you either divide or complete the square.

1. The major axis is the variable with the largest deno.

2. The minor axis is the variable with the smallest deno.

3. The vertex is the square root of the largest deno. To put in pt form, if the major axis is x the answer goes in the x spot and vice versa.

4. The other intercept is the square root of the smallest deno. Then put in pt form.

5. The length of the major axis is 2 X the square root of largest deno.

6. The length of the minor axis is 2 X the square root of the smallest deno. The focus is always on the major axis and is a pt.

7. To find the focus, vertex, or the other intercept use the formulas below. Smallest deno = largest deno – focus^2.OR Other intercept^2 = vertex^2 – focus^2.

Ex.

1. x^2/25 + y^2/4 = 1

1. x

2. y

3. +/- 5 (5,0) (-5,0)

4. +/- 2 (0,2) (0,-2)

5. 2 X square root of 25 = 10

6. 2 X square root of 4 = 4

7. 4 = 25 – f^2

-25 -25

-21 = -f^2

f^2 = 21

f = square root of 21

(square root of 21,0) (-square root of 21,0)