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Re: Week of 'date' - Monday (use day of week that you are posting notes)

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Checked homework and then worked on WKST "Solving Equations Review", which is due the day of our next test.

Chapter 10 Section 3 Circles

Warm- Up

x= -1/2y^2

2. Find the vertex, directrix, and focus.

vertex: (0,0)
directrix: x = 1/2
focus: (-1/2,0)

Circles

Formula:  x^2 + y^2 = r^2

y^2 = 8 - x^2
y^2 + x^2 = 8
r^2 = 8
r = sqr rt(8) = 2* sqr rt(2)

(-2,5)

1. Find the equation of the cirle which contains this point.

r = sqr rt ((-2)^2 + 5^2) = sqr rt(29)
x^2 + y^2 = (sqr rt(29))^2
r^2 = 29
x^2 + y^2 = 29

2. Find the equation of the line which passes through this point and it tangent to the cirlce.

(5-0)/(-2-0) = -5/2

y - 5 = 2/5 (x+2)

3. A light pole gives of light that can be seen from a 30 yds radius of the light pole.  You are 10 yds east and 25 yds south of the light pole.

a) Give an inequality of the amount the amount of light that can be seen.
      x^2 + y^2 < 900

b) Can you see light from the position you are at?
     yes

c) How many miles north would you have to walk to not be able to see the light?
     53.284 yds

We checked our homework in the first half of class. #80 on page 599 was on the board: "In the drawing shown at the left, the rays of the sun are lighting a candle. If th candle is 12 inches from the back of the parabolic reflector and the reflector is 6  inches deep, then what is the diameter of the reflector?

diagram:

The answer should be about 34 in. Know how to do this problem.

 After, we worked on Cricles with Sliders in Excel. Note: on the OSP, there is a document called Inserting an Increment Button Scroll-Bar.doc

Horizontal equation:               

Vertical equation:

 b²+c²=a²

 Write equation in standard form and find foci: 4x²+25y²=100
(4x²/100)+(25y²/100)=1
(x²/25)+(y²/4)=1
(x²/5²)+(y²/2²)=1

Therefore, a=5, and b=2. To find foci, plug the values for a and b into the equation
b²+c²=a².
2²+c²=5²
4+c²=25
c²=21
c=sqrt(21)
The focus is (sqrt(21), 0)

 Write an equation when a focus is (2,0), and the vertices are (4,0) and (-4,0).

If one focus is (2,0), the other must be (-2,0).

If a=4, c=2, then b²+2²=4².
b²+4=16
b²=12

Plug this value and the value of a into the horizontal equation. (x²/16)+(y²/12)=1.

An elliptical garden is 32 feet long and 14 feet wide. Write an equation and find the area.

a=16, and b=7.
(x²/16²)+(y²/7²)=1

To find area, use the formula A=abп
So, (16)(7) п=A
A≈351.858 ft²

Hyperbolas

https://myfiles.st-agnes.org/Users/Students/jmckinney/%231.bmp

transverse axis- axis that the vertices are on

https://myfiles.st-agnes.org/Users/Students/jmckinney/%232.bmp

(x^2/a^2) - (y^2/b^2) = 1

https://myfiles.st-agnes.org/Users/Students/jmckinney/%233.bmp

(y^2/a^2) - (x^2/b^2) = 1

https://myfiles.st-agnes.org/Users/Students/jmckinney/%234.bmp

center to focus = c   and   b to a = c

a^2 + b^2 = c^2

4x^2 - 9y^2 = 36
(4x^2 - 9y^2 = 36)/36
(x^2/3^2) - (y^2/2^2) = 1
a = 3  b = 2 

https://myfiles.st-agnes.org/Users/Students/jmckinney/%235.bmp

a = 2  c = 3
a^2 + b^2 = c^2
4 + b^2 = 9
b^2 = 5
(y^2/4) - (x^2/5) = 1

https://myfiles.st-agnes.org/Users/Students/jmckinney/%236.bmp