9.3 Graph & Write Equations of Circles 3/25 Day 2
9.3 Graph & Write Equations of Circles 3/25 Day 2
9.3 Graph & Write Equations of Circles 3/25 Day 2
Lesson2.notebook March 25, 2014
9.3 Graph & Write Equations of Circles 3/25
Day 2
Ex. 3: What is an equation of a line tangent to the circle
x2 + y2 = 13 at (3, 2)?
Inequalities: x2 + y2 < r2 represents the region inside the circle,
and x2 + y2 > r2 represents the region outside the
circle.
Ex. 4: Write a circular model
A cellular phone tower services a 10 mile radius. You get
a flat tire 4 miles east and 9 miles north of the tower. Are
you in the tower's range?
Step 1: Write an inequality
Step 2: Substitute the coordinates
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Math Lesson2.notebook March 25, 2014
Ex. 5: In ex. 4, suppose you fix your tire and drive south. For
how many more miles will you be in range of the tower?
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Math Lesson2.notebook March 25, 2014
Review
9.6 Translating Circles: (x h)2 + (y k)2 = r2
**the center of the circle is at the point (h, k)
Ex. 1: Graph (x 2)2 + (y + 3)2 = 9
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Math Lesson2.notebook March 25, 2014
Name
Mar. 25, 2014
Hour
p. 630 #5658e, 62, 69, p.655 #4, 8
Write an equation of the line tangent to the given circle at the given point.
56. x2 + y2 = 40; (6, 2)
58. x2 + y2 = 250; (15, 5)
62. A cellular phone tower services a 15 mile radius. On a hiking trip,
you are 9 miles east and 11 miles north of the cell tower. Are you in
the region served by the tower?
69. Two radio transmitters, one with a 40 mile range and one with a 60
mile range stand 80 miles apart. You are driving 60 miles per hour
on a highway parallel to the line segment connecting the two towers.
How long will you be within range of both transmitters
simultaneously?
Graph the equation.
4. (x 2)2 + (y 7)2 = 9
8. (x 5)2 + (y + 1)2 = 64
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Math Lesson2.notebook March 25, 2014
HOMEWORK HELP!!
p. 630 #5658e, 62, 69, p.655 #4, 8
Write an equation of the line tangent to the given circle at the given point.
56. x2 + y2 = 40; (6, 2)
Radius Slope: m = 2 0 = 1/3
6 0
Perpendicular slope = opposite reciprocal = 3
y y1 = m(x x1)
y (2) = 3(x (6))
y + 2 = 3x 18
y = 3x 20
69. Two radio transmitters, one with a 40 mile range and one with a 60
mile range stand 80 miles apart. You are driving 60 miles per hour
on a highway parallel to the line segment connecting the two towers.
How long will you be within range of both transmitters
simultaneously?
10 mi