Chapter 10
10.1 Distance and Midpoint Formula
Goal 1 To find the distance between two points in a plane
Goal 2 To find the coordinates of the midpoint of a
segment given the endpoints
149
6 2
 3, 5 


 2 2
 9, 5
HW #10.1
Pg 431-432 1-15 Odd, 17-27
Chapter 10
10.2 Conic Sections Circles
Goal 1 To find the equation of a circle given the radius
and the coordinates of the center of the circle.
Goal 2 To find the radius and coordinates of the center of
the circle given the equation of the circle
Circle
Hyperbola
Ellipse
Parabola
C
B
D
F
E
A
HW #10.2
Pg 436-437
1-15 odd, 16-26, 28-31
Chapter 10
10.3 Ellipses

(a,0)

F (c,0)
(0, b)
P( x, y )


F (c, 0)
1
2

(0, b)
(a,0)

(a,0)

F1 ( c,0)
(0, b)
P( x, y )


F2 (c,0)

(0, b)
a  c  a  c  2a
(a,0)

(a,0)

F1 ( c,0)
(0, b)
P( x, y )


F2 (c,0)

(0, b)
(a,0)

(a,0)

F (c,0)
(0, b)
P( x, y )


F (c, 0)
1
2

(0, b)
(a,0)

a
a
(a,0)

P(0, b)
b

F1 ( c,0)
c
(a,0)

F2 (c,0)
 (0, b)
a b c
2
2
2
c 2  a 2  b2
a 2  b2  c 2
b2  a 2  c 2
Center of
the Ellipse
c2 = a 2 – b2
Draw theelipsegivenby 4 x 2  9 y 2  16 x  18 y  11  0
Identify the center, vertices and foci.
HW #10.3
Pg 442-443 1-23 Odd, 25-34
Chapter 10
10.4 Hyperbolas
HW #10.4
Pg 450-451 1-23 Odd, 24-30
Chapter 10
10.5 Parabolas
Definition: Parabola
The set of all points in a plane that are equidistant from a
fixed point F and a fixed line. The point is the Focus and
the line is the Directrix
The book uses p for a so it would be y2 = 4px
Theorem 10-10
A parabola with focus at (0, p) and vertex at (0, 0) has
directrix y = -p
Theorem 10-11
The standard form of a parabola with focus at (0, p),
directrix y = -p, vertex (0, 0), and y-axis as the only line
of symmetry is x2 = 4py
Theorem 10-11
The standard form of a parabola with focus at (p, 0),
directrix x = -p, vertex (0, 0), and x-axis as the only line
of symmetry is y2 = 4px
The vertex is midway between the focus and the directrix
The vertex is midway between the focus and the directrix
The vertex is midway between the focus and the directrix
Write the standard form of the equation of the parabola
that satisfies the given conditions
Focus: (4, 0); Directrix x = -4
y2 = 16x
Focus: (-4, 2); Directrix x = -6
(y - 2)2 =4(x + 5)
Focus: (-4, 2); Vertex (-4, 5)
(x + 4)2 =-12(y - 5)
HW #10.5
Pg 456-457 1-37 Odd, 38-41
Chapter 10
10.6 Second Degree Equations and
Systems
hyperbola
parabola
parabola
ellipse
circle
hyperbola
( x  3)  ( y  1)  16
2
2
2
x  y
3
2
( y  3) 2 ( x  1) 2

1
4
1
The solutions appear to be
(4,3) and (-4,-3).
The solutions appear to be (5,0) and (-5,0).
(4, 3) and (-3, -4)
(-2, 0) and (2, 0)
(4, 7) and (-1, 2)
(4, 0) and (-4, 0)
HW #10.6
Pg 462-463 1-39 Odd 41-43
Chapter 10
10.7 Solving Quadratic Systems
Algebraically
Substitute x = 2 and x = -3 into the linear equation and solve
for y.
Substitute x = 2 and x = -3 into the linear equation and solve
for y.
Find the points of intersection of the graphs in the system
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.
You can eliminate the y2-term by adding the two equations.
Find the points of intersection of the graphs in the
system.
HW #10.7
Pg 467-468 1-25 Odd, 26-30
Chapter 10
10.8 Using Systems of Second
Degree Equations
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
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.
6x8
About 1.41 Miles
The epicenter of the earthquake is 50 miles due west
of the first seismograph
HW #10.8
Pg 471 10-18
Test Review
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.
1. Find an equation for the outline of this elliptical chain wheel.
2. What is the area of the chain wheel.
HW #R-10
Pg 475-477 1-33 Odd