Ellipses :)

This week in class we learned 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.

Step 1: The major axis is the variable with the largest denominator.

Step 2: The minor axis is the variable with the smallest denominator.

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

Step 4: The other intercept is the square root of the smallest denominator. Then put in point form.

Step 5: The length of the major axis is 2 times the square root of largest denominator.

Step 6: The length of the minor axis is 2 times the square root of the smallest denominator.

-The focus is ALWAYS on the major axis and is a POINT.

Step 7: To find the focus, vertex, or the other intercept use the formulas below.

-Smallest denominator = largest denominator – focus^2

-Other intercept^2 = vertex^2 – focus^2

Example:

1.) x^2/4 + y^2/9 = 1

step 1: y

step 2: x

step 3: +/- 3 (0,3) (0,-3)

step 4: +/- 2 (2,0) (-2,0)

step 5: 2 X square root of 9 = 6

step 6: 2 X square root of 4 = 4

step 7: small deno = large deno – f^2

4 = 9 – f^2

-9 -9

-5 = -f^2

f^2 = 5

f = square root of 5

(0, square root of 5) (0, -square root of 5)

THE END :)