Chapter 10 study guide
1) A circle has a diameter with endpoints (4,2) and
(-2,4).
Find the coordinates of the center, length of the
radius, and area.
Find the center, vertices, co-vertices, foci, and
asymptotes for each hyperbola and graph:
9)
x2
9
y2
16
1
2) Write the equation of a circle with center (-1,2)
and radius 4. Graph the circle.
10)
3) Write an equation of the line tangent to the
2
2
circle x 6
y 1
25 at the point (2, 4)
Find an equation of the hyperbola described:
y 2
1
2
x 1
4
2
1
11) Center 0,0 , Vertex
4) Write the equation of the circle with center
(-5, -2) and containing the point (19, -9)
5) Write an equation in standard form for each
ellipse with center (0.0)
a) Vertex (6,0) and co-vertex (0,-5)
7,0 , Co-vertex 0,5
12) Center 0,0 , focus 5, 0 , asymptotes y
13) Foci
3, 2 and
3
x
4
3,8 , vertex ( 3,7)
b) Co-vertex (-24, 0) and focus (0, -18)
Find the vertex, axis of symmetry, focus, and directrix
of each parabola and then graph:
c) Co-vertex (0, -24) and focus (10, 0)
14) 4 x
6) Graph each ellipse.
a)
( x 4) 2
25
15) x 2
( y 1) 2
64
1
y2 4 y
8 y 4x 4 0
Find the equation of the parabola described:
16) Focus (0, 0) , directrix y
b)
( x 2)
49
2
( y 3)
16
4
2
1
17) Vertex 0,0 , directrix x 1 0
7) Find the constant sum of an ellipse with foci
F1 2,3 and F2 5, 1 and the point on the
18) Focus 3, 4 Vertex 3, 2
ellipse 2,3 .
Identify the conic by completing the square and graph
– label all appropriate parts:
8) Engineers have designed a tunnel with the
x2 y 2
1 , measured in feet. A design
equation
81 64
for a larger tunnel needs to be twice as wide and 3
times as tall. Find the dimensions for the larger
tunnel and write an equation for the design of the
larger tunnel.
19) x 2
y 2 12 x 4 y 32 0
20) 4 x 2
25 y 2 24 x 50 y 89 0
21) 3x 2
4 y 2 18 x 8 y 19 0