### CIRCLES AND ELLIPSES REVIEW PROBLEMS

```Name:_______________________________________________________________
Chapter 9 Review
CIRCLES:
1.
State the coordinates of the center and find the radius of each circle whose equation is given.
a)
b)
2.
3.
x2  ( y  2)2  4
16
( x  7) 2  y 2 
25
C ___________, r = _____
C ___________, r = _____
Write the equation of a circle for the given center and radius. Write it in BOTH circle AND elliptical form.
a)
C(-1, -5), r = 2
b)
C(-3, 5), r =
_________________________________
6
_________________________________
Write an equation of a circle that passes through the given point P and whose center is the given point C.
a)
b)
P(2, -1); C(5, 7)
P(-1, -4); C(-1, 0)
4*.
Write an equation of a circle tangent to the y-axis, that has its center at (-8, -7).
5.
Write an equation of a circle given the endpoints of one of its diameters. (2, 3) and (5, -2)
6*.
The equation of a circle and a point on the circle is given. Write an equation of the line that is tangent to the circle
at that point.
9.
a)
a)
x2  y 2  13 ,
(-2, -3)
b)
x2  y 2  24 ,
(-2
2 , -4)
Write an equation for each graph.
b) Use r=3 even though the graph is a bit off.
10.
Find the coordinates of the center and the radius of each circle whose equation is given. Graph each.
a)
b)
c)
d)
x2  y 2  49
x2  y 2  6 y  16  0
e)
x2  y 2  9 x  8 y  4  0
( x  2)2  ( y  3)2  25
x2  y 2  4 x  9
ELLIPSES:
1.
Find the coordinates of the center, foci, vertices and co-vertices, and find the
lengths of the major and manor axis.
a)
c)
e)
2.
b)
d)
x2 y 2

1
5 10
( x  3)2 ( y  1)2

1
4
9
The equation of an ellipse is given. Find the coordinates of the center and state
whether the major axis is vertical or horizontal.
a)
3.
x2 y 2

1
25 9
( x  1)2 ( y  11) 2

1
121
144
5x 2 + 25y 2 = 125
x2 y 2

1
5 20
b)
( x  4) 2 ( y  6) 2

1
42
23
Write an equation of an ellipse given the following.
a)
b)
Center (0, 0); Vertex at (7, 0); Co-Vertex at (0, 5)
Foci at (  3, 0) and Vertices at (  6,0)
c)
d)
Foci at (0,  17 ) and Co-Vertices at (  8, 0)
Foci on the x-axis, Major Axis 9 units long and Minor Axis 4 units long, the
center is (0, 0)
The endpoints of the Major Axis are at (10, 2) and (-8, 2). The foci are at
(6, 2) and (-4, 2)
e)
4.
Write an equation for the ellipse.
5.
Graph the following ellipses. Label the vertices, co-vertices, and foci.
a)
c)
( x  5) 2 ( y  11) 2

1
121
144
x2  5 y 2  4 x  70 y  209  0
b)
d)
( x  8)2 ( y  2) 2

1
81
1
10x2+30y2=90
6. Consider an elliptical room that is 5 feet wide (y) and 7 feet long (x) . Write an
equation to model the room and find the area of the room to the nearest tenth.
7. Put in standard form. Is it an ellipse or a circle? If it is an ellipse, identify the center,
vertices, co-vertices, major axis, minor axis, and foci. If it is a circle, identify the center
2
2
a) 4 x  9 y  16 x  18 y  11  0
b) 7x2+7y2+14x+28y=-7
c) x2+3y2+y=9
8.
x2  y2 + 4x  4 = 0
x2 + y2  3x + 3 = 0
9.
x2 + 2y2  3y = 0
x2 + y 2  2 = 0
10. 2x2  y2  x  4 = 0
x2 + y2 + 3x  4 = 0
11. 2x2 + 3y2 = 1
x2 + y2 +4 = 0
Hyperbolas and Parabolas
1. Find the vertex, focus and directrix of x 
1 2
y 8  0
48
2. The cross section of a television antenna dish is a parabola and the receiver is located at the focus. If the
receiver is located 5 feet above the vertex (assume the vertex is at the origin), find an equation for the cross
section of the dish. If the dish is 10 feet wide, how deep is it?
3. If another television antenna is available that is 2.5 feet deep with the same width as question #2, where is
For #4-6, find an equation of each parabola having the given characteristics.
4. vertex (2, -3) and focus (2, -1)
5. vertex (5, 2) and directrix y 
3
2
6. focus (-1, 3) and directrix y = 2
7. Find the vertex, focus, and directrix of the parabola whose equation is f ( x) 
out the leading coefficient, and complete the square.)
1 2
x  3 x  11 . (Hint: Factor
4
8. Graph  y 2  2 x . Identify the focus and directrix.
9. Write 6 y 2  4 x 2  36 y  8 x  26 in standard form.
10. Natural draft cooling towers are shaped like hyperbolas for more efficient cooling of power plants. The
x2 y 2

 1 , where the units are in meters. Find the
hyperbola in the tower at the right can be modeled by
16 225
width of the tower at the top and its narrowest point in the middle.
11. Graph
 x  2
2
  y  3  1 .
2
9
Identify the center, vertices, foci, and asymptotes, as well as the length of the
transverse axis..
12*. Graph xy = 12. How would the graph of xy=-12 look different?


13. Write the equation of the hyperbola given: vertices (-5, 0) and (5, 0) and foci  26, 0 . Write the
equations of the asymptotes.
14. Identify the vertices, foci, and asymptotes of
 y  2
4
2

 x  3
4
2
1
.
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