Graph the equation of a translated circle

1
EXAMPLE 1
Graph the equation of a translated circle
Graph (x 2)2 (y 3) 2 9.
SOLUTION
STEP 1
2
EXAMPLE 1
Graph the equation of a translated circle
STEP 2
Plot the center. Then plot several points that
are each 3 units from the center
(2 3, 3) (5, 3)
(2 3, 3) (1, 3)
(2, 3 3) (2, 0)
(2, 3 3) (2, 6)
STEP 3
Draw a circle through the points.
3
EXAMPLE 2
Graph the equation of a translated hyperbola
Graph

1
SOLUTION
STEP 1
Compare the given equation to the standard forms
of equations of hyperbolas. The equations form
tells you that the graph is a hyperbola with a
vertical transverse axis. The center is at (h, k)
(1, 3). Because a2 4 and b2 9, you know
that a 2 and b 3.
4
EXAMPLE 2
Graph the equation of a translated hyperbola
STEP 2
5
EXAMPLE 2
Graph the equation of a translated hyperbola
STEP 3
Draw the hyperbola. Draw a rectangle centered at
(1, 3) that is 2a 4 units high and 2b
6 units wide. Draw the asymptotes through the
opposite corners of the rectangle. Then draw the
hyperbola passing through the vertices and
approaching the asymptotes.
6
for Examples 1 and 2
GUIDED PRACTICE
Graph (x 1)2 (y 3) 2 4.
1.
SOLUTION
circle with center at (h, k) ( 1, 3) and
radius r 2
7
for Examples 1 and 2
GUIDED PRACTICE
Graph (x 2)2 8 (y 3) 2.
2.
SOLUTION
parabola with vertex at (2, 3) ,focus (2, 1)
and directrix y 5
8
for Examples 1 and 2
GUIDED PRACTICE
Graph
3.
(x 3)2

1
SOLUTION
hyperbola with vertices (4, 4) and (2, 4),
asymtotes y 2x 2 and y 2x 10
9
for Examples 1 and 2
GUIDED PRACTICE
(x 2)2
Graph
4.

1
16
SOLUTION
Ellipse with center (2, 1), vertices (6, 1) and
(2,1) and covertices (2, 4) and (2, 2)