648 CHAPTER 11 Nonlinear Functions, Conic Sections, and Nonlinear Systems
28.An ellipse can be drawn on a piece of posterboard by fasten-
ing two ends of a length of string with thumbtacks, pulling
the string taut with a pencil, and tracing a curve, as shown in
the figure. Explain why this method works.
Graph each ellipse. See Examples 5 and 6.
31. 32.
33. 34.
35. 36.
37. 38.
39. 40.
41.Explain why a set of ordered pairs whose graph forms an ellipse does not satisfy the def-
inition of a function.
- (a)How many points are there on the graph of? Explain.
(b)How many points are there on the graph of? Explain.
EXERCISES 43 AND 44
43.The circle shown in the calculator graph was
created using function mode, with a square viewing
window. It is the graph of
What are the two functions and that were used
to obtain this graph?
44.The ellipse shown in the calculator graph was
graphed using function mode, with a square viewing
window. It is the graph of
What are the two functions and that were used
to obtain this graph?
Use a graphing calculator in function mode to graph each circle or ellipse. Use a square
viewing window. See the Connections box.
47. 48.
1 x- 322
25
+
y^2
9
= 1
x^2
16
+
y^2
4
= 1
x^2 +y^2 = 36 1 x- 222 +y^2 = 49
y 1 y 2
x^2
4
+
y^2
9
=1.
y 1 y 2
1 x+ 222 + 1 y- 422 =16.
TECHNOLOGY INSIGHTS
1 x- 422 + 1 y- 122 =- 1
1 x- 422 + 1 y- 122 = 0
1 x+ 322
25
+
1 y+ 222
36
= 1
1 x- 222
16
+
1 y- 122
9
= 1
1 x- 422
9
+
1 y+ 222
4
= 1
1 x+ 122
64
+
1 y- 222
49
= 1
y^2
9
= 1 -
x^2
16
y^2
25
= 1 -
x^2
49
x^2
49
+
y^2
81
= 1
x^2
16
+
y^2
4
= 1
x^2
9
+
y^2
4
= 1
x^2
36
+
y^2
16
= 1
x^2
9
+
y^2
16
= 1
x^2
9
+
y^2
25
= 1
10
–10
4
–4
–6 6
