10.1 Distance and Midpoint Formula

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Chapter 10

• 10.1 Distance and Midpoint Formula

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HW 10.1 Pg 431-432 1-15 Odd, 17-27
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Chapter 10

• 10.2 Conic Sections Circles

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Circle
Ellipse
Hyperbola
Parabola
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D
F
C
E
A
B
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HW 10.2 Pg 436-437 1-15 odd, 16-26, 28-31
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Chapter 10

• 10.3 Ellipses

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Center of the Ellipse
c2 a2 b2
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Identify the center, vertices and foci.
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HW 10.3 Pg 442-443 1-23 Odd, 25-34
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Chapter 10

• 10.4 Hyperbolas

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HW 10.4Pg 450-451 1-23 Odd, 24-30
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Chapter 10

• 10.5 Parabolas

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The book uses p for a so it would be y2 4px
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The vertex is midway between the focus and the
directrix
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The vertex is midway between the focus and the
directrix
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The vertex is midway between the focus and the
directrix
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Write the standard form of the equation of the
parabola that satisfies the given conditions
y2 16x
Focus (4, 0) Directrix x -4
(y - 2)2 4(x 5)
Focus (-4, 2) Directrix x -6
(x 4)2 -12(y - 5)
Focus (-4, 2) Vertex (-4, 5)
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HW 10.5Pg 456-457 1-37 Odd, 38-41
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Chapter 10

• 10.6 Second Degree Equations and Systems

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hyperbola
parabola
parabola
ellipse
circle
hyperbola
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The solutions appear to be (4,3) and (-4,-3).
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The solutions appear to be (5,0) and (-5,0).
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(4, 7) and (-1, 2)
(4, 3) and (-3, -4)
(4, 0) and (-4, 0)
(-2, 0) and (2, 0)
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HW 10.6Pg 462-463 1-39 Odd 41-43
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Chapter 10

• 10.7 Solving Quadratic Systems Algebraically

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Substitute x 2 and x -3 into the linear
equation and solve for y.
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Substitute x 2 and x -3 into the linear
equation and solve for y.
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Find the points of intersection of the graphs in
the system
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Because Equation 2 has no x2-term, solve that
equation for x.
Next, substitute 2y2 - 2 for x in Equation 1 and
solve for y.
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You can eliminate the y2-term by adding the two
equations.
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Find the points of intersection of the graphs in
the system.
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HW 10.7Pg 467-468 1-25 Odd, 26-30
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Chapter 10

• 10.8 Using Systems of Second Degree Equations

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Two square pieces of plastic together have an
area of 100 square inches. When a square the
size of the smaller piece is cut from the larger
piece, the remaining area is 28 square inches.
What are the lengths of the sides of the two
squares?
Larger Square is 8 x 8 Smaller Square is 6 x 6
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A rectangular beam with a cross-sectional area 48
in2 is cut from a circular log with diameter 10
inches. Find the dimensions of the beam.
6 x 8
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About 1.41 Miles
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The epicenter of the earthquake is 50 miles due
west of the first seismograph
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HW 10.8Pg 471 10-18
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Test Review
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The pedals of a bicycle drive a chain wheel,
which drives a smaller sprocket wheel on the rear
axle. Many chainwheels are circular. However,
some are slightly elliptical, which tends to make
pedaling easier. The front chain wheel on the
bicycle shown below is 8 inches at its widest and
7½ inches at its narrowest.

• Find an equation for the outline of this
  elliptical chain wheel.
• What is the area of the chain wheel.

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HW R-10Pg 475-477 1-33 Odd
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