6-4 Hyperbolas

This week we learned section 6-4. Section 6-4 was dealing with hyperbolas

Hyperbolas are in the form x^2/a^2 –y^2/b^2 or –x^2/a^2 + y^2/b^2.

Part of the Equation:
1. Major axis – variable with larger denominator (non-negative)
2. Minor axis –variable with smaller denominator
3. Length of major –2 square root of non-negative denominator
4. Length of minor –2 square root of smaller denominator
5. Vertex – square root of non-negative denominator
If x is major: (_,0) and (-_, 0)
If y is major: (0,_) and (0, -_)
6. Other intercepts – square root of smaller denominator … ( , ) opposite of vertex
7. Focus – focus squared = larger denominator + smaller denominator
If x is major: (focus, 0)
If y is major: (0, focus)
8.Asymptotes –
If x is major: y = +/- b/ax
If y is major: y = +/- a/bx


Examples:

X^2?25-Y^2/100=1

1. x
2. y
3. 10
4. 20
5. (5,0)(-5,0)
6. (0,10)(0,-10)
7. (5square root of 5,0)( -5square root of 5,0)
8. y= + and – 2x


Basically if you know your rules and stuff it easy and it the same thing as 6-3 rules but couple new steps to 6-4 that all.

6-4

Sooo I hope everyone had an awesome time at prom this weekend. I can’t remember if we did hyperbolas this week cause we only had one day of learning this week. The rest of the week we did aleks. So I’m just gonna do section 6-4 hyperbolas.

In the form x2/a – y2/ = 1 or –x2/a2 + y2/b2/

Parts of the equation
-Major axis : variable with larger denominator
-Minor axis: variable with smaller denominator
-Length of major: 2 square root non negative denominator
-Length of minor: 2 square root smaller denominator
-Vertex: square root non negative denominator if x is major (_,0 )and (-_,0); if y is major (0,_) and (0,-_)
-Other intercept: smaller denominator ( , ) Opposite of vertex
- Focus: focus2 = larger denominator and smaller denominator if x is major (focus,0) if y is major (0,focus)
-Asymtoles: y = +/-b/ax if x is major, y = +/-a/bx if y is major

solving the system

Okay, so this might be a little short because there was only one thing we learned this past week because we did aleks for the rest of the days. The 28 aleks that we are supposed to do are going to be very difficult to finish since we didn’t get to work in the library on Thursday. Once im done with this, Ill probably be working on that until I fall asleep. Also with prom this weekend, this is the first chance I am having to start on my schoolwork. I hope everyone had a great time (: On Wednesday, we learned something from algebra II called solving the system.

Honestly, I tried a bunch of different times to work a problem to put on here but all of the different numbers I tried just would not work out. They all came out with big fractions that I just don’t know how to complete. Im sorry I couldn’t figure it out but it is a pretty simple process whenever you already have a problem given to you. (This blog is over 150 words though)

6-4

Prom is this weekend, tonight actually and I’m stressin’ big time! So this might be a little short..
Section 6-4 dealt with hyperbolas. Hyperbolas are in the form x^2/a^2 –y^2/b^2 or –x^2/a^2 + y^2/b^2.
Parts of the equation are similar to the ellipse.
1. Major axis – variable with larger denominator (non-negative)
2. Minor axis – variable with smaller denominator
3. Length of major – 2*square root of non-neg denominator
4. Length of minor – 2*square root of smaller denominator
5. Vertex – square root of non-neg denominator
If x is major: (_,0) and (-_, 0)
If y is major: (0,_) and (0, -_)
6. Other intercepts – square root of smaller denominator … ( , ) opposite of vertex
7. Focus – focus squared = larger denominator + smaller denominator
If x is major: (focus, 0)
If y is major: (0, focus)
**SOMETHING DIFFERENT: Asymptotes –
If x is major: y = +/- b/ax
If y is major: y = +/- a/bx

EXAMPLE 1: x^2/9 – y^2/16 Find all parts.
1. x (since 16 is negative)
2. y
3. 2*square root of 9 = 6
4. 2*square root of 16 = 8
5. square root of 9 = (3, 0) and (-3,0)
6. square root of 16 = (0,4) and (0,-4)
7. 9 + 16 = 25
focus = 5
8. y = +/- 4/3x

Hope everyone has a fun, memorable weekend!

a matrices review..

Prom is next saturday:D but im sure you guys already know :) im kinda excited about it too. But anyways,I cant seem to find my chapter six notes so ill blog about something we did a while back. Matrices, yayyy. Just like every other area of advanced math, matrices are tedious.

Here are the matrices rule:

When adding matrices, they must be of the same dimensions. The same goes for subtracting

Ex. A 4x3 matrices can only be added to a 4x3 matrices

When multiplying matrices, you can only multiply matrices that have the same columns and rows.

Ex. 3x3* 1x2 the column of the first are equal to the rows of the second.

You cannot technically divide a matrices, to "divide" a matrices, you simply multiply by the inverse..

finding the inverse.

0 1

1 0 = 0-1=-1 = 1/-1* 0 1

1 0 = 0 -1

-1 0

Zomg

Zomg. Look who finally remembered that blogs exist!

So this week in Advanced Math we started chapter six, but we skipped 6-1 because B-Rob said it was dumb. So, one thing we learned was section 2 which is all about connics and the equation of a circle.

First, you must remember how to complete a square. To complete a square, you must put it in standard form. Then, get rid of the coefficient of x^2 or y^2. Next, divide the middle term by 2 and square it. Add the number to both sides. Then factor in (x )^2 form.

The mid point formula is also needed for this. As a remindered, it's (Xv1+ Xv2)/2, (Yv1+Yv2)/2.

The distance formula is used as well when given a center point and an outside point.

The equation of a circle is (x-h)^2 +(y-k)^2 = r^2 where (h,k) is the center.

Example of how to make an equation--
C=(4,3) r=2
(x-4)^2 + (y-3)^2 = 4

Example of finding coordinates of the point where the lines intersect--
y= 2x-2 and circle x^2 +y^2=25
By calculator:
plug in y=2x-2 and y= + or - square root (25-x)^2
Then hit graph
Then hit second trace
The click a point on the top circle
Then a point on the line
Then guess where about they intersect.
Answer-
(3,4)

Chapter 6

Guess what we did this week? Yup, you guessed it, Math. We did Math this week, but not just any kind of Math, Advanced Math. and not just any old Advanced Math but Elipsises. Which, come to think of it, is very hard to pronounce in the plural sense of the word. Anyway, enough stalling just so I can reach the 150 word thing, no I would never do such a terrible thing.

Ellipses have many parts.

Major axis- Found by whcih axis has the larger denominator
Minor axis- Found by which axis has amaller denominator
Length of the major axis- Found with the equation. 2xSquare root(larger denominator)
Length of the minor axis-.............................................................(Smaller denominator)
Intercepts, major and minor- Is the square root(Larger denominator) or (smaller denominator). Takes place of corresponding variable, depending on which is major, the other variable is 0
Focus- I think its Larger Denominator=Smaller Denominator+Focus squared