Exercise Set 8.1: Parabolas
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 a parabola, where the
standard form is represented by one of the following
equations:
() ()
24xh pyk−= −
() ()
24xh pyk−=− −
() ()
24yk pxh−= −
() ()
24yk pxh−=− −
1. 214 2 43 0yyx−−+=
2. 210 12 61xxy+−=−
3. 2
9810yx x−=−−
4. 2
71024xy y−= − +
5. 2
32450xy y=−+
6. 2
21215yx x=++
7. 2
335 0xx y−−−=
8. 2
55 6yyx+=−
For each of the following parabolas,
(a) Write the given equation in the standard form
for the equation of a parabola. (Some
equations may already be given in standard
form.)
It may be helpful to begin sketching the graph for
part (h) as a visual aid to answer the questions
below.
(b) State the equation of the axis.
(c) State the coordinates of the vertex.
(d) State the equation of the directrix.
(e) State the coordinates of the focus.
(f) State the focal width.
(g) State the coordinates of the endpoints of the
focal chord.
(h) Sketch a graph of the parabola which includes
the features from (c)-(e) and (g). Label the
vertex V and the focus F.
9. 240xy−=
10. 212 0yx−=
11. 2
10
x
y−=
12. 2
6
y
x−=
13.
()()
2
285xy
−
=+
14.
()
2
416yx−=
15.
(
)
243yx
=
−
16.
()()
2
341xy
+
=−
17.
(
)
2
(5) 2 4xy
+
=− −
18.
() ()
2
1103yx
+
=− +
19.
() ()
2
612yx
−
=− −
20.
() ( )
2
186xy
−
=− −
21. 212 6 24 0xxy
+
−+=
22. 22810xyx
−
=−
23. 28436yxy
−
=+
24. 26450yyx
+
−+=
25. 225 16 10
x
yx+=− −
26. 210 28 0yyx
+
++ =
27. 24240yyx
−
+−=
28. 2
12 4 16yx x
+
−=−
29. 2
3308670yyx
+
−+=
30. 2
5301619xxy
+
−=
31. 2
28734xxy−+ =
32. 2
489400yyx
−
++=
Use the given features of each of the following
parabolas to write an equation for the parabola in
standard form.
33. Vertex:
(
)
2, 5−
Focus:
(
)
4, 5
34. Vertex:
(
)
1, 3
−
Focus:
(
)
1, 0
