6-3 Ellipses

I am going to show you how to sketch ellipses. There are 7 easy steps on how to get the information so you can sketch your ellipse. I will show you an example problem and step by step how to solve the ellipse and how to sketch it. The steps are really easy to follow and i will also explain each step. The most important part of an ellipse is to know the standard form which is x^2/a^2 + y^2/b^2= 1. If a^2 has the bigger number then x is major axis. if b^2 has the bigger number then y is the major axis. once you find which one is major axis and minor axis then you are ready to finish the 7 steps and continue to graph the ellipse which i will demonstrate in the example problem. The other thing that is really important to do is to graph correctly or else your answer will be completely wrong.


Example: x^2/9 + y^2/16= 1 Sketch the graph.
step 1: find major axis: y
step 2: find minor axis: x (because a^2 is smaller than the b^2)
step 3: take the square root of the largest denomenator: square root of 16= 4. then you put in point form. if major axis is x is goes in x spot and vice versa. (0,4) (0,-4)
step 4: take the square root of the smallest denomenator: square root of 9= 3 (3,0) (-3,0)
step 5: find length of the major axis: 2* square root of largest denom: 2* square root of 16= 2(4)= 8
step 6: find length of the minor axis: 2* square root of smallest denom: 2* square root of 9= 2(3)= 6
step 7: find the focus. the focus goes on the major axis. smallest denom=largest denom - focus^2: 9=16 - f^2= the square root of 7. point form: (0,square root 7) (0,-square root 7)


Now that you have havethe information it's time to graph.