This week in advanced math we started on chapter 6. In section three we learned about ellipses. Ellipses appear in the form of x2/a + y2/b = 1. Parts of the equation of ellipses are:

Major axis – the variable with the larger denominator
Minor axis – the variable with the smaller denominator
Length of the major axis – 2 square root of the larger denominator
Length of the minor axis – 2 square root of the smaller denominator
Vertex – square root of the larger denominator if x is major (_,0) and (-_,0) and if y is major (0,_) (0,_)
Other intercept – square root of smaller denominator ( ,) Opposite of vertex
Focus – Smaller denominator = larger denominator, focus2 is x is major (0, focus) (focus,0)

Example 1:
x2/9 + y2/36 = 1

1) Major axis - y
2) Minor axis – x
3) Length of Major – 2 square root 36 = 12
4) Length of Minor – 2 square root 9 = 6
5) Vertex – (0, 6) (0, -6)
6) Other intercept – (3,0) (-3,0)
7) Focus – 9 = 36 –f2 =-27 = square root 27 (0, square root 27) (0,-square root 27)

This past week we learned some of Chapter 6.

6-2
CONICS

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

D=square root of (y2-y1)^2 + (x2-x1)^2 = r

-get rid of coefficient of x^2 or y^2
-divide middle term by 2 and square it.
-add to both sides
-factor to (x)^2

EXAMPLE:
(x-7)^2 + (y+2)^2=25
CENTER: (7,-2)
RADIUS: square root of 25 = 5

6-3
ELLIPSES

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

PARTS OF THE EQUATION:
major axis-variable with larger denominator

minor axis-variable with smaller denominator

length of major-2 square root of larger denominator

length of minor-2 square root of smaller denominator

vertex-if x is major ( ,0) & ( ,0)
if y if major (0, ) & (0, )

other- opp. of vertex ( , )

focus- smaller denom. = larger denom. - focus^2
if x is major (0, focus)
if y is major (focus, 0)

6-3

This week we learned section 6-3. In 6-3 we learned how to solve problems in the form of x^2/a+y^2=1

Part of the Equations:

Major axis

Minor axis

length of major

length of minor

Vertex

Other Int

Focus


Examples: Find all the parts of X^2/4+y^2/25=1

1. Major axis= y
2. Minor axis=z
3 Length of major=10
4. length of minor=4
5. vertex= (0,5)(0,-5)
6. Other Int=(2,0)(-2,0)
7. focus=( 0,square root of 21)(0,-square root of 21)

Basically if you know all your steps and procedure you will not have any problem at this section and this will be a breeze for you to.

6-3

This week in advanced math we learned how to find parts of the equation. The equation has many parts and we learned how to identify them all. We also learned recently how to find the equation of the circle. This is done by finding the distance formula and plugging numbers in the right place into the equation. But in this we'll focus on 6-3 and finding parts of the equation.

In the form x^2/a + y^2/b = 1

Parts of the equation

x^2/9 + y^2/16 = 1

major axis- y

minor axis- x

length of major-2 the square root of 16 = 2(4)= 8

length of minor- 2 the square root of 9 = 2(3) = 6

vertex - (0,4) and (0,-4)

other int - (3,0) and (-3,0)

focus - 9-16 = f^2 -7=f^2 f= square root of -7

chapter 6

This week we did some pretty easy things in chapter 6 for the most part. The easiest thing for me personally is finding the 7 parts of an ellipse.
1. Tell the major axis
2. Tell the minor axis.
3. Length of major
4. Length of minor
5. Vertex
6. Other intercepts
7. Focus
All of these things are pretty easy to find.

Ex: x^2/25 + y^2/9 = 1
^^ all of them must equal 1.

1. Major axis- x because the number on the bottom is bigger
2. Minor axis-y
3. Length of major – 10 (2 times the square root)
4. Length of minor- 6
5. Vertex – (5,0) (-5,0) (square root of the major axis. The number goes in the x spot since it is larger.
6. Other intercepts- (0,3)(0,-3)
7. focus- 4 ( smaller denominator = larger denominator – f^2)

6-3

This week in advanced math we are learning how chapter 6 which is ellipses, conics, and hyperbolas. I don't find this very hard. All you need to do if follow the steps which you're teacher has given you. Today I will show you how to find an ellipse equation and all that good stuff.

**This is the form of an ellipse equation: x^2/a + y^2/b


Step or parts of ellipse equation:

1. Major axis is the variable with larger denominator.
2. Minor axis is the variable with smaller denominator.
3. Length of major is 2 times the square root of larger denominator
4. Length of minor is 2 times the square root of smaller denominator.
5. Vertex is square root of larger denominator.

If x is major you should use this (_,0) and (-_, 0).
If y is major you should use this (0,_) and (0, -_).

6. Other intercepts is square root of smaller denominator ( , ) opposite of vertex.
7. Focus is the smaller denominator = the larger denominator – the focus squared.

If x is major you should use this (0, focus).
If y is major you should use this (focus, 0).

EXAMPLE 1: Find all the parts of x^2/4 + y^2/16.
1. y
2. x
3. 8
4. 4
5. (0,4) (0,-4)
6. (2,0) (-2,0) 6. 7 = 16 – focus squared
focus = (0,3) (0,-3)

This is how you find the equation thingy or whatever to an ellipse.

6-3

6-3 Ellipses
This past week we learned about conics, ellipses, and hyperbolas.
Ellipses are in the form: x^2/a + y^2/b

Parts of the equation:
1. Major axis – variable with larger denominator
2. Minor axis – variable with smaller denominator
3. Length of major – 2*square root of larger denominator
4. Length of minor – 2*square root of smaller denominator
5. Vertex – square root of larger 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 – smaller denominator = larger denominator – focus squared
If x is major: (0, focus)
If y is major: (focus, 0)

EXAMPLE 1: Find all the parts of x^2/9 + y^2/25.
1. y
2. x
3. 2 * the square root of 25 = 10
4. 2 * the square root of 9 = 6
5. Since y is the major, (0,5) and (0,-5)
6. (3,0) and (-3,0) 7. 9 = 25 – focus squared
focus = +/- 4 therefore, (0,4) and (0,-4) is your focus.