Merry Christmas and Happy Ellipses.

So here’s the deal guys, I didn’t know what to blog about and the first thing I saw upon opening my binder was ellipses so that sounded like a good topic. Time to review.

Standard form of an ellipse is as follows:

x^2/a^2+y^2/b^2=1

Put an ellipse into standard form by dividing or completing the square. Dividing is a lot easier, trust me.

1.Define the major axis (The variable with the largest denominator is major)

2. Define the minor axis (The variable with the smaller denominator is minor)

3. Find the vertex. The vertex is the square root of the major axis (larger denominator).It is put into point form. The answer goes into the slot of the major axis.

4. Find the other intercept. The other intercept is the square root of the minor axis (smaller denominator). It is put into point form and the answer goes into the slot of the minor axis.

5. Find the length of the major axis. This is found by multiplying the square root of the major axis by two.

6. Find the length of the minor axis. This is found by multiplying the square root of the major axis by two.

7. Find the focus. (The focus is ALWAYS on the major axis.) It is in point form. The equation for finding the focus, vertex, or other intercept is smallest denom=largest denom-focus^2.

EXAMPLE

Sketch the ellipse.

X^2/49+y^2/64=1

1. Y is major.

Again, the larger denominator is the major axis.

2. X is minor.

The smaller denominator is the minor axis.

3. Vertex=square root of 64=+/-8 (0,8) (0,-8)

The vertex will always be the square root of the major axis put into point form and you better not forget that or I will be very upset with you.

4. Other intercept=square root of 49=+/-7 (7,0) (-7,0)

The other intercept is, obviously, always the square root of the minor axis put into point form.

5. 2*square root of 64=16

6. 2*square root of 49=14

7. 49=64-f^2
f^2=15
f=+/-square root of 15 (0, square root of 15) (0, square root of 15)

THE FOCUS IS ALWAYS ON THE MAJOR AXIS.

You would, of course, graph it afterwards.

That’s our review.

I hope everyone had a great Christmas and has an awesome new year. See you guys soon (:
--Sarah