Exercise Set 8.3: Hyperbolas
Math 1330, Precalculus
The University of Houston Chapter 8: Analytic Geometry
Identify the type of conic section (parabola, ellipse,
circle, or hyperbola) represented by each of the
following equations. (In the case of a circle, identify
the conic section as a circle rather than an ellipse.) Do
NOT write the equations in standard form; these
questions can instead be answered by looking at the
signs of the quadratic terms.
1. 2
290yx x++=
2. 22
14 7 12 6 95xxy y+− =− +
3. 22
735 40xyxy−=−+
4. 299
y
yx+= −
5. 22
373 1213xxy y−+ =− +
6. 22
10 2 5xxyy+=−−+
7. 22
42869yxyx+=−+
8. 22
824830yxx+=+
Write each of the following equations in the standard
form for the equation of a hyperbola, where the
standard form is represented by one of the following
equations:
()()
22
22
1
xh yk
ab
−−
−=
()()
22
22
1
yk xh
ab
−−
−=
9. 22
880yx−−=
10. 22
310 300xy−−=
11. 22
623
x
yx y−−=−−
12. 22
9 3 48 192xy y−= +
13. 22
7 5 14 20 48 0xy xy−++−=
14. 22
9 2 90 16 175 0yx yx−+++=
Answer the following.
15. The length of the transverse axis of a hyperbola
is __________.
16. The length of the conjugate axis of a hyperbola is
__________.
17. The following questions establish the formulas
for the slant asymptotes of
()()
22
22
1
yk xh
ab
−−
−
=.
(a)
State the point-slope equation for a line.
(b) Substitute the center of the hyperbola,
(
)
,hk into the equation from part (a).
(c) Recall that the formula for slope is
represented by rise
run . In the equation
()()
22
22
1
yk xh
ab
−−
−
=, what is the “rise” of
each slant asymptote from the center? What
is the “run” of each slant asymptote from the
center?
(d) Based on the answers to part (c), what is the
slope of each of the asymptotes for the graph
of
()()
22
22
1
yk xh
ab
−−
−
=? (Remember that
there are two slant asymptotes passing
through the center of the hyperbola, one
having positive slope and one having
negative slope.)
(e) Substitute the slopes from part (d) into the
equation from part (b) to obtain the
equations of the slant asymptotes.
18. The following questions establish the formulas
for the slant asymptotes of
()()
22
22
1
xh yk
ab
−−
−
=.
(a)
State the point-slope equation for a line.
(b) Substitute the center of the hyperbola,
(
)
,hk into the equation from part (a).
(c) Recall that the formula for slope is
represented by rise
run . In the equation
()()
22
22
1
xh yk
ab
−−
−
=, what is the “rise” of
each slant asymptote from the center? What
is the “run” of each slant asymptote from the
center?
(d) Based on the answers to part (c), what is the
slope of each of the asymptotes for the graph
