

1. 
If rectangle ABCD has vertices A(0, 0), B(a, 0), and C(a, b), find the coordinates of D. 


A. 
(a, 0) 
B. 
(0, b) 


C. 
(0, b) 
D. 
(0, 3) 


Hint 


2. 
Write the general form of the equation of the circle that passes through the points at (4, 2), (–3, 1), and (–2, –6). 


A. 
x^{2} + y^{2} – 2x – 4y + 20 = 0 


B. 
x^{2} + y^{2} – 2x + 4y – 20 = 0 


C. 
x^{2} + y^{2} + 2x – 4y – 20 = 0 


D. 
x^{2} + y^{2} + 2x + 4y – 20 = 0 


Hint 


3. 
Write the equation of the ellipse whose center is at the origin, a = 6, and . 


A. 



B. 



C. 
or 


D. 
or 


Hint 


4. 
Find the equation of the hyperbola with foci at (8, 2) and (4, 2) whose transverse axis is 10 units long. 


A. 

B. 



C. 

D. 



Hint 


5. 
Find the standard form of the equation x^{2}  5y^{2}  2x  10y  9 = 0. 


A. 

B. 



C. 

D. 



Hint 


6. 
Write the equation of the parabola whose vertex is at (6, 2) and whose focus is at (4, 2). 


A. 
(y  2)^{2} = 40(x  4) 
B. 
(x  2)^{2} = 40(y + 6) 


C. 
(y  2)^{2} = 40(x + 6) 
D. 
(x  2)^{2} = 40(y + 6) 


Hint 


7. 
Identify the conic section represented by the equation 2x^{2}  6x + 2y^{2} + 12y + 18 = 0. 


A. 
ellipse 
B. 
parabola 


C. 
circle 
D. 
hyperbola 


Hint 


8. 
In the general equation of a conic, B = 0, A = C = 1, D = 4, E = 6, and F = 4. Write the equation in standard form. 


A. 
(x  2)^{2} + (y + 3)^{2} = 9 
B. 
(x  2)^{2} + (y  3)^{2} = 9 


C. 
(x  3)^{2} + (y  2)^{2} = 9 
D. 
(x  3)^{2} + (y + 2)^{2} = 9 


Hint 


9. 
Write an equation in general form of y = x^{2}  x + 5 for T_{(1, 2)}. 


A. 
x^{2}  3x  y  5 = 0 
B. 
x^{2}  3x  y + 5 = 0 


C. 
x^{2} + 3x  y + 5 = 0 
D. 
x^{2}  3x + y + 5 = 0 


Hint 


10. 
Solve the system of equations algebraically. x  y + 2 = 0 x^{2} + y^{2} = 10 


A. 
(1, 3), (3, 1) 
B. 
(4, 6) 


C. 
(1, 3) 
D. 
(3, 1), (1, 3) 


Hint 


11. 
Graph the system of inequalities and . 


A. 

B. 



C. 

D. 



Hint 


12. 
Find the distance between points (5, 4) and (2, 3). Round to the nearest tenth. 


A. 
14 
B. 
9.9 


C. 
7.1 
D. 
3.2 


Hint 


13. 
Write the equation of a circle that passes through points (1, 2), (1, 4) and (3, 2) in standard form. 


A. 
(x + 1)^{2} + (y  2) ^{2} = 4 


B. 
(x  1) ^{2} + (y + 3) ^{2} = 4 


C. 
(x + 1) ^{2} + (y  3) ^{2} = 4 


D. 
(x  1) ^{2} + (y  2) ^{2} = 4 


Hint 


14. 
Write an equation of an ellipse with foci at (2, 0) and (2, 0) and a = 4. 


A. 



B. 



C. 



D. 



Hint 


15. 
Find the vertex of the parabola with equation of x^{2} = 3y + 12. 


A. 
(4, 0) 
B. 
(12, 0) 


C. 
(0, 12) 
D. 
(0, 4) 


Hint 


16. 
Write an equation in general form of for T_{(2,3)}. 


A. 



B. 



C. 



D. 



Hint 

