6-3 ELLIPSES

Ch.6, Section 3-Ellipses
Before you can begin sketching an ellipse, you must either complete the square or divide to get your equation in standard form.


The first step in sketching an ellipse is finding your major axis. Your major axis will be the variable with the largest denominator.

Next, you will state your minor axis. Your minor axis is the variable with the smallest denominator.

Now you will find your vertex. You start by finding the square root of the largest denominator. After you've done that, you must put it in point form. If the major axis is x, then your answer will go in the x coordinate spot. If your answer is y, then it goes in the y coordinate spot.

To find your other intercept, you must square root your smallest denominator. Your answer will go in point form just as your vertex.

Next, you have to find the length of your major axis. To do this, you must multiply 2 by the square root of the largest denominator.

Now you find the length of your minor axis. You do the same as you did to find your major, except you multiply 2 by the square root of your smallest denominator.

The last thing you do before actually sketching your ellipse is finding the focus. To find the focus, you use the equation, smallest denominator = largest denominator - focus^2(squared). Your focus will always be a point on the major axis.




EX: (x^2/4)+(y^2/9)=1

1) y is major because is has the larger denominator

2) x is minor because it has the smaller denominator

3) square root of 9 is +/-3, vertex =(0,3) (0,-3)

4) square root of 4 is +/-2, other intercept =(2,0) (-2,0)

5) 2 x square root of 9 = 6, lenth = 6

6) 2 x square root 4 = 4, length = 4

7) 4 = 9 - focus^2
= square root of -5 = square root of focus^2
= +/-2.2
Focus = (2.2,0) (-2.2,0)


And this is how to solve an ellipse :) -JORDAN