1. EXAMPLE 1 Graph the equation of a translated circle Graph (x – 2) 2 + (y + 3) 2 = 9. SOLUTION STEP 1 Compare the given equation to the standard form of an equation of a circle. You can see that the graph is a circle with center at (h, k) = (2, – 3) and radius r = 9= 3.

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 (y – 3) 2 4 – (x + 1) 2 9 = 1 SOLUTION STEP 1 Compare the given equation to the standard forms of equations of hyperbolas. The equation’s form tells you that the graph is a hyperbola with a vertical transverse axis. The center is at (h, k) = (– 1, 3). Because a 2 = 4 and b 2 = 9, you know that a = 2 and b = 3.

4. EXAMPLE 2 Graph the equation of a translated hyperbola STEP 2 Plot the center, vertices, and foci. The vertices lie a = 2 units above and below the center, at (21, 5) and (21, 1). Because c 2 = a 2 + b 2 = 13, the foci lie c = 13 3.6 units above and below the center, at (– 1, 6.6) and (– 1, – 0.6).

5. EXAMPLE 2 Graph the equation of a translated hyperbola STEP 3 Draw the hyperbola. Draw a rectangle centered at (21, 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. GUIDED PRACTICE for Examples 1 and 2 Graph (x + 1) 2 + (y – 3) 2 = 4. SOLUTION STEP 1 Compare the given equation to the standard form of an equation of a circle. You can see that the graph is a circle with center at (h, k) = (– 1, 3) and radius r = 4 = 2. 1.

7. GUIDED PRACTICE for Examples 1 and 2 (– 1 + 2, 3) = (1, 3)(– 1 – 2, 3) = (– 3, 3) (– 1, 3 + 2) = (– 1, 5)(– 1, 3 – 2) = (– 1, 1) STEP 3 Draw a circle through the points. STEP 2 Plot the center. Then plot several points that are each 2 units from the center:

8. GUIDED PRACTICE for Examples 1 and 2 Graph (x – 2) 2 = 8 (y + 3) 2. SOLUTION STEP 1 Compare the given equation to the standard form of an equation of a parabola. You can see that the graph is a parabola with vertex at (2, – 3), focus (2, – 1) and directrix y = – 5 2.

9. GUIDED PRACTICE for Examples 1 and 2 STEP 2 Draw the parabola by making a table of value and plot y point. Because p > 0, he parabola open to the right. So use only points x- value x12345 y–2.875–3– 2.875–2.5– 1.875 STEP 3 Draw a circle through the points.

10. GUIDED PRACTICE for Examples 1 and 2 Graph (x + 3) 2 – (y – 4) 2 9 = 1 SOLUTION STEP 1 Compare the given equation to the standard forms of equations of hyperbolas. The equation’s form tells you that the graph is a hyperbola with a vertical transverse axis. The center is at (h, k) = (– 3, 4). Because a 2 = 1 and b 2 = 4, you know that a = 1 and b = 2. 3.

11. GUIDED PRACTICE for Examples 1 and 2 STEP 2 Plot the center, vertices, and foci. The vertices lie a = 1 units above and below the center, at (–2, 4) and (–4, 4). Because c 2 = a 2 + b 2 = 5, the foci lie c = 5 units above and below the center, at (– 3, +,4 ) and (– 3, –, 4). 5 5

12. GUIDED PRACTICE for Examples 1 and 2 STEP 3 Draw the hyperbola. Draw a rectangle centered at ( –3, 4) that is 2a = 2 units high and 2b = 4 units wide. Draw the asymptotes through the opposite corners of the rectangle.

13. GUIDED PRACTICE for Examples 1 and 2 Graph (x – 2) 2 16 + (y – 1) 2 9 = 1 SOLUTION STEP 1 Compare the given equation to the standard forms of equations of hyperbolas. The equation’s form tells you that the graph is a hyperbola with a vertical transverse axis. The center is at (h, k) = (2, 1). Because a 2 = 16 and b 2 = 9, you know that a = 4 and b = 3. 4.

14. GUIDED PRACTICE for Examples 1 and 2 Plot the center, vertices and co-vertices. Vertices are at (h + a,k) are (6,1) and ( – 2,1) and co-vertices are at (h,k +b) are (2,4) and (2,– 2) STEP 2 STEP 3 Draw the ellipse that panes through each vertices and co-vertices