MTH 112 Sec 8.5B, circles, parabolas 060209.notebook
June 02, 2009
MTH 112 - June 2, 2009
1.
Today we will . . .
- go over HW from 8.3
- finish polar coordinates (8.5)
- start conic sections (circles and then parabolas, if time)
2.
New HW (all out of the supplemental packet)
Conics (CIRCLES)
p.3: 2, 3, 6, 11 - 13
Conics (PARABOLAS)
pp.8-9: 2, 4, 5, 9
Conics (ELLIPSES)
pp.14-16: 2, 4 - 7, 9
Conics (HYPERBOLAS)
p.22: 1 - 4
Note: Answers to odd-numbered problems are in the back.
3.
Next (and LAST!!) HW Quiz is tomorrow
Will cover 7.3, 7.5, 7.6, 8.1 - 8.3
4.
Remember . . . .
Your Final is WEDNESDAY, June 10
12:00 - 1:50 pm.
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MTH 112 Sec 8.5B, circles, parabolas 060209.notebook
June 02, 2009
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MTH 112 Sec 8.5B, circles, parabolas 060209.notebook
June 02, 2009
Sections 8.5 ­ Polar Coordinates (cont.)
Points can represented with angles in radians or degrees. Angles can be more than one revolution.
o
90
60o
Plot the points
45o
A (­2, 450o) B (4, ­135o)
30o
Give two more representations for each point.
180o
0o
How many different representations of each point are there?
270o
How do polar coordinates relate to rectangular coordinates?
(r, θ )
This picture looks familiar! What is it like?
r
θ
So...to convert from polar coordinates to rectangular you use
x =
y =
EXAMPLE: Convert (­2, 150o) to rectangular coordinates.
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MTH 112 Sec 8.5B, circles, parabolas 060209.notebook
What about converting rectangular coordinates to polar coordinates?
June 02, 2009
Using the same picture...
r =
(x, y)
and r
θref =
y
θ
x
Remember to consider the quadrant to get the true value of θ !
EXAMPLE: Find polar coordinates for 1. (−5, 4)
2. (2, −7)
Conics got their name because they can be made by intersecting a plane with a double cone.
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MTH 112 Sec 8.5B, circles, parabolas 060209.notebook
June 02, 2009
What is a circle?
How do we get its equation?
Every point (x, y) on the circle is a distance of r from the center (h, k). Use the distance formula
to find the standard equation.
(x, y)
(h, k)
r
The standard equation of a circle with radius r and center (h, k) is
(x ­ h)2 + (y ­ k)2 = r 2
Find the equation of a circle with radius 7 and center (2, ­5)
Find the equation of a circle whose diameter has endpoints (­3, 4) and (5, 8).
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MTH 112 Sec 8.5B, circles, parabolas 060209.notebook
June 02, 2009
What if the equation of a circle is not in "standard form"?
EXAMPLE: A circle has equation x2 + y2 ­ 10x + 8y + 32 = 0. What are its center and radius?
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