Algebra 2
1.
a)
b)
c)
Chapter 12 Review Name___________________
Write an equation for a circle with the given characteristics:
center (-6, 9) and radius 4
center (-5, -1) and radius 5
center (0, 3) and radius 9
2. Write the equation of the line that is tangent to the given circle and at the
given point.
a) (x - 2)2 + (y – 1) 2 = 25; (-1, -3)
b) (x + 3)2 + (y + 6)2 = 144; (-3, 6)
3. Write the equation of the ellipse with center at (0, 0).
a) vertex (0, 5) and co-vertex (-2, 0)
b) vertex (61, 0) and focus (60, 0)
c) co-vertex (-20, 0) and focus (0, 48)
4. Graph the ellipse.
a) (x + 2)2 + (y – 3)2 = 1
9
16
b) (x – 8)2 + (y + 3)2 = 1
81
49
5. Write the equation of the hyperbola in standard form with center at (0, 0).
a) co-vertex (0, -9) and focus (-41, 0)
b) vertex (8, 0) and co-vertex (0, -2)
c)
6.
a)
b)
c)
d)
e)
f)
d)
Given the following parts find the equation of the parabola in standard form.
v(3, 4) and directrix: y = 2
v(-2, 1) and focus (-1,1)
v(0, 5) and directrix: x = -2
v(2, -3) and focus (2, -2)
focus (-6, 0) and directrix x = 6
focus (-1, 0) and directrix x = 3
7. Find the vertex, value of c, axis of symmetry, focus, directrix of each parabola ,
then graph.
a) y - 3 = 2(x – 5)2
b) x + 1 = (1/12)(y + 2)2
c) y + 2 = -4(x + 3)2
8. Write the equation for the parabola, and give its domain and range, then graph.
a) Focus (-1, 0) and directrix x = 5
b) Focus (0, -6) and directrix y = 6
9. Put the following ellipse in standard form.
a) 3x2 + 2y2 – 18x + 21 = 0
b) x2 + 4y2 – 2x – 16y + 1 = 0
10. Put the following circles in standard form. Find the center and the radius.
a) x2 + y2 + 2x +10y + 1 = 0
b) x2 + y2 – 4x + 6y – 3 = 0
11. Solve the system of equations.
a) x – 2y = 0
x2 + y2 = 125
b) 8y = x + 5
x + 5 = (1/2)y2
12. Solve.
a) 5 + 3√x + 2 = 14
c) 20x2 + x - 12 = 0
e) (161/2)-1/2
b) -4 - 2√x – 3 = 8
d) 12x2 – 17x – 5 = 0
e) (32)-3/5
13. Identify the following (Ellipse, Parabola, Circle, Hyperbola, line, other)
a) 2x + 3y = 7
b) 16x2 – y2 – 4y – 68 = 0
c) x2 – 6y + y2 + 5 = 0
d) y2 + 8x + 2y + 57 = 0
e) x2 – 9y2 + 2x + 18y – 17 = 0
f) x2 + y2 – 4x + 4y – 17 = 0
g) x2 + 4y2 – 2x – 16y + 1 = 0
h) x = -2y + 3
i) 2x2 + 2y2 – 36x – 2y + 162 = 0
j) 4y2 + x – 12y + 12 = 0