Exercise Set 8.2: Ellipses
Math 1330, Precalculus
The University of Houston Chapter 8: Analytic Geometry
Write each of the following equations in the standard
form for the equation of an ellipse, where the standard
form is represented by one of the following equations:
()()
22
22
1
xh yk
ab
−−
+=
()()
22
22
1
xh yk
ba
−−
+=
1. 22
25 4 100 0xy+−=
2. 22
9161440xy+−=
3. 22
936432640xxyy−+− +=
4. 22
4241632120xxyy++ −−=
5. 22
3 2 30 12 87xy xy+−−=−
6. 22
8 113 14 48
x
yxy++=+
7. 22
16 16 64 8 24 42xx y y−−=−− +
8. 22
18 9 153 24 6
x
yxy+=−+
Answer the following.
9. (a) What is the equation for the eccentricity, e,
of an ellipse?
(b) As e approaches 1, the ellipse appears to
become more (choose one):
elongated circular
(c) If 0e=, the ellipse is a __________.
10. The sum of the focal radii of an ellipse is always
equal to __________.
Answer the following for each ellipse. For answers
involving radicals, give exact answers and then round
to the nearest tenth.
(a) Write the given equation in the standard form
for the equation of an ellipse. (Some equations
may already be given in standard form.)
It may be helpful to begin sketching the graph for
part (g) as a visual aid to answer the questions
below.
(b) State the coordinates of the center.
(c) State the coordinates of the vertices of the
major axis, and then state the length of the
major axis.
(d) State the coordinates of the vertices of the
minor axis, and then state the length of the
minor axis.
(e) State the coordinates of the foci.
(f) State the eccentricity.
(g) Sketch a graph of the ellipse which includes
the features from (b)-(e). Label the center C,
and the foci F1 and F2.
11. 22
1
949
xy
+
=
12. 22
1
36 4
xy
+
=
13.
()
22
21
16 4
xy
−
+
=
14.
()
2
211
95
y
x+
+
=
15.
()()
22
23
1
25 16
xy−+
+
=
16.
()()
22
52
1
16 25
xy++
+
=
17.
()()
22
43
1
91
xy+−
+
=
18.
()()
22
23
1
36 16
xy++
+
=
19.
()()
22
24
1
11 36
xy−+
+
=
20.
()()
22
35
1
20 4
xy+−
+
=
21. 22
49360xy
+
−=
22. 22
41xy
+
=
23. 22
25 16 311 50 64
x
yxy+−=−
24. 22
16 25 150 175xy y+=+
25. 22
16 32 4 40 52 0xxy y
−
+−+=
26. 22
25 9 100 54 44 0xy xy
+
−+−=
27. 22
16 7 64 42 15 0xy xy
+
+−+=
28. 22
43166290xy xy
+
−+−=
