math home work
FK1987
math_hw_8.doc1. Eliminate t to determine what type of conic is described by the parametric equations:
(a)
x
t
=
7
sin
,y
t
=
3
cos
.(b)
x
t
=
-
+
2
3
sin
,y
t
=
-
5
6
sin
(c)
x
t
=
2
tan
,y
t
=
+
3
8
sec
2. Convert the polar equation to rectangular form and identify:
(a)
r
=
-
35
2
7
sin
q
(b)
q
p
=
4
3. Find an equation for the parabola whose focus is at (-2,6) and whose directrix is the line y = -2.
What are the coordinates of the vertex?
Draw a graph of the parabola.
4. Find an equation for the parabola with horizontal axis of symmetry if it passes through the points (5,0), (14,1), and (5,-2).
5. For the conic whose equation is
0
44
16
72
4
12
2
2
=
+
-
+
-
y
x
y
x
(a) Identify the conic:
(b) Complete the square and write the conic in standard form:
(c) Sketch the graph:
6. Find an equation for the ellipse whose graph is
y
End points of major axis (2,-3) and (2,9).
Length of minor axis: 6.
______________________x
7. Identify and graph the conic:
(a)
r
=
+
3
4
4
sin
q
(b)
q
cos
2
5
15
+
=
r
8. Use the discriminant
AC
B
4
2
-
to decide whether the equation represents a parabola, an ellipse, or a hyperbola:(a)
0
4
5
4
12
3
2
2
=
-
-
+
+
-
y
x
y
xy
x
(b)
0
6
25
3
4
2
=
-
+
+
-
y
x
xy
x
(c)
0
450
90
30
4
2
2
=
+
-
-
+
+
y
x
y
xy
x
(d)
0
6
4
3
3
2
2
2
=
-
+
-
+
-
y
x
y
xy
x
