Elipses

The standard form of an elipse is: x^2/a^2+y^2/B^2=1

*When you put in standard form, either divide or complete the square.


When you sketch an elipse:



1. Find the major axis. The major axis is the variable with the largest denominator.

2. Find the minor axis. The minor axis is the variable with the smallest denominator.

3. Find the vertices. In order to find the vertex, you find the square root of the largest denominator.

**To put in standard form, if the major axis is "x", the answer goes in the ''x'' spot, and vice versa.

4. Now you need to find the other intercept. To find this, you must square the smallest denominator.

***Put this into point form. (#,#)

5. Find the length of the minor axis by using two times the square root of the smallest denominator.

6. Find the length of the major axis by using two times the square root of the largest denominator.

7. Now you need to find the focus. The focus is always on the major axis and is always a point.

-To find the vertex, focus, or other intercept use:
smallest denominator=largest denominator-focus ^2
or
other intercept^2=vertex^2-focus^2



Example 1:

(x^2/36)-(y^2/16)

1. Major axis-X

2. Minor axis-Y

3. Square root of 36= 6

4. Square root of 16= 4

5. 2 times the square root of 36=12

6. 2 times the square root of 16= 8

7. 52=36-f2
f2=16