x - MathnMind

Your Notes
Example 1 Graph the equation of a translated circle
Graph (x 1 3) 2 1 (y 2 2) 2 5 4.
1. Compare the given equation to
the standard form of an equation
of a circle. The graph is a circle
with center at (h, k) 5 ( , )
and radius r 5 Ï }
5 .
2. Plot the center. Then plot several
points that are each units
from the center:
Copyright © Holt McDougal. All rights reserved. Lesson 9.6 Algebra 2 Notetaking Guide 249
5
5
5
5
3. Draw a circle through the points.
Example 2 Graph the equation of a translated hyperbola
Graph
(y 1 2)2
}
16
2 (x 2 1)2
}
4
5 1.
1. Compare the given equation to the standard forms
of equations of hyperbolas. The graph is a hyperbola
with a transverse axis. The center is at
(h, k) 5 ( , ). Because a2 5 and
b2 5 , you know that a 5 and b 5 .
2. Plot the center, vertices, and foci.
y
The vertices lie a 5 units
above and below the center, at
2
( , ) and ( , ).
2
x
Because c2 5 a2 1 b2 5
the foci lie c 5 Ï
,
}
ø
units above and below the center,
at ( , ) and ( , ).
3. Draw the hyperbola. Draw a rectangle centered at
( , ) that is 2a 5 units high and 2b 5
units wide. Draw the asymptotes through the opposite
corners of the rectangle. Then draw the hyperbola so
that it passes through the vertices and approaches the
asymptotes.
1
y
1 x