objectives: students will be to… identify the center and the radius of a circle from its equation...
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11.5: Circles in the Coordinate
Plane
Objectives: Students will be to…• Identify the center and the radius of a
circle from its equation• Write and graph the equation of a
circle
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A set of all points in a plane that are a given
distance, the radius, from a given point, the center
Circle
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Standard equation of a circle with center (h,
k) and radius r
(x – h)2 + (y – k)2 = r2
Standard Equation of a Circle
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h = -1k= 3r = 2Plug values into standard equation:
(x – (-1))2 +(y – 3)2 = (2)2
(x + 1)2 + (y-3)2 = 4
notice #’s are opposite sign of what is given
Write the equation of the circle with center (-1,3) and a radius of 2.
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a.) center (3,5); radius = 6
b.) center (-2,-1); radius =
c.) center (0, 0); radius = 5
Write the equation of the circle with the given center and radius.
2
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You can use this to find the radius of a circle and write the equation.
If r2 = (x-h)2 + (y – k)2, then….
22 )()( kyhxr
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h = 2k= 3x= -1y= 1
Write the standard form of the circle with center (2,3) that passes through the point (-1,1).
22 )( kyhxr
22 3121 r
22 23 r
1349 rWrite the equation using h, k, and r:
1332
133222
222
yx
yx
Write the equation for finding radius
Substitute h,k, x and y into equation.
Simplify parenthesis
Find radius by adding numbers under radical
Remember, squaring a square root gets rid of the square root
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1.) center (-2,6); point (-2, 10)
2.) center (7, -2); point (1, -6)
Write the standard form of the circle with the given center that passes through the given point.
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Find the center and radius of the circle Plot the center Draw radius. Use compass to draw circle with
the given radius.
Graphing a circle:
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(x + 7)2 + (y -5)2 = 16
h= -7k= 5r= 4
Center (-7, 5), radius = 4
Find the center and radius of the circle with the given equation. Then graph the circle.
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x2 + y2 = 9
Find the center and radius of the circle with the given equation. Then graph the circle.
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(x – 2)2 + (y – 3)2 = 100
Find the center and radius of the circle with the given equation. Then graph the circle.
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A diagram locates a radio tower at (6, -12) on a coordinate grid where each unit represents 1 mile. The radio signal’s range is 80 miles. Find an equation that describes the position and range of the tower.
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Write the equation of the circles graphed below: