math home work

1. Elimina

t

e 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

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