Ellipses

Standard form of an ellipse is x^2/a^2+y^2/b^2=1.

To find the equation of an ellipse, use these 7 steps.

1. First find which variable is the major axis. This will be the one with the largest denominator.

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

3. Next find the vertex(the square root of the largest denominator). When putting this in point form, if the major axis is x, put the vertex in the x spot, and vice versa.

4. The other intercept is the square root of the smallest denominator. Put this point in the spot of the minor axis.

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

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

7. To find the focus, use this formula: smallest denominator=largest denominator+focus^2.

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Example problem:

Sketch the equation. x^2/100+y^2/64=1.

1. x is the major axis because 100 > 64.

2. y is the minor axis because 64 < 100.

3. The vertex is + or - 10 because that's the square root of 100. When putting this in point form, put the 10 and -10 in the x spot (10,0), (-10,0) because x is the major axis.

4. The other intercept is + or - 8. (0,8), (0,-8).

5. The length of the major axis is 2 times the square root of 100, which is 20.

6. The length of the minor axis is 16.

7. The focus is + or -6. (6,0), (-6,0).
64=100-f^2
-100 -100

(-f^2=-36)* -1

sqrt f^2= sqrt 36

f=+ or -6.