Section 1.5 Circles - Montgomery Collegefaculty.montgomerycollege.edu/maronne/Ma180/power...
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Section 1.5 Circles Copyright © 2013 Pearson Education, Inc. All rights reserved
Transcript of Section 1.5 Circles - Montgomery Collegefaculty.montgomerycollege.edu/maronne/Ma180/power...
Section 1.5
Circles
Copyright © 2013 Pearson Education, Inc. All rights reserved
Copyright © 2013 Pearson Education, Inc. All rights reserved
Copyright © 2013 Pearson Education, Inc. All rights reserved
Copyright © 2013 Pearson Education, Inc. All rights reserved
Copyright © 2013 Pearson Education, Inc. All rights reserved
Write the standard form of the equation of the circle with radius 4 and center (2, –4).
( ) ( )2 22 4 16x y− + + =
Copyright © 2013 Pearson Education, Inc. All rights reserved
Copyright © 2013 Pearson Education, Inc. All rights reserved
( ) ( )2 2Graph the equation: 4 1 9x y− + + =
( ) ( )2 2 2(4 1) 3x y −+ − =−
( ) ( )2 2 2h rx y k+ − =−
( )Center: 4, 1 Radius: 3−1 2 3 4 5 6 7
4
−3
−2
−1
1
2
3
x
y
( )4, 1−
Copyright © 2013 Pearson Education, Inc. All rights reserved
( ) ( )2 2For the circle 4 1 9, find the intercepts, if any, of its graph.
x y− + + =
( ) ( )2 2-intercepts: 0 4 1 9x x + + =−
( )2 84x − = 8 24 2x − = ± = ±
4 2 2x = ± 6.83 and 1.17x x≈ ≈
-intercepts: We can see looking at the graph that there are no-intercepts. If we attempted to find them we'd get no real solutions.
yy
1 2 3 4 5 6 7
4
−3
−2
−1
1
2
x
( )4, 1−
( )4 2 2,0− ( )4 2 2,0+
Copyright © 2013 Pearson Education, Inc. All rights reserved
Copyright © 2013 Pearson Education, Inc. All rights reserved
Copyright © 2013 Pearson Education, Inc. All rights reserved
2 2Graph the equation: 8 4 5 0x y x y+ − + − =
2 28 __ 4 __ 5 __ __x x y y− + + + + = + +
2 216 4 6 48 4 15x x y y− + + + + = + +
( ) ( )2 24 2 25x y− + + =
( )Center: 4, 2 Radius: 5−
−2 −1 1 2 3 4 5 6 7 8 9 10 11
−9
−8
−7
−6
−5
−4
−3
−2
−1
1
2
3
4
x
y
( )4, 2−
Copyright © 2013 Pearson Education, Inc. All rights reserved
Copyright © 2013 Pearson Education, Inc. All rights reserved
