August 16, 2020
August 16, 2020

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MAC 1147 TEST 4 REVIEW
LESSONS 8, 9, 10, 11
1. Find focus, directrix, and graph
A. x
2 = -9py
B. x
2 = 2p7
C. y
2 = 6px
D. y
2 = -4px
2. Wriye the equation of the parabola given vertex at (0,0) and directrix at x=4.
3. Find focus, vertex, and graph each ellipse.
A. π₯
2
16
+
π¦
2
49
= 1 B. π₯
2
81
+
π¦
2
16
= 1
4. Write the equation of an ellipse with focus at (5,0) and vertices at (8,0), centered at
(0,0).
5. Find focus, vertices, asymptotes, and graph each hyperbola
A. π₯
2
16
β
π¦
2
9
= 1 B. π¦
2
36
β
π₯
2
9
= 1
6. Find the equation of a hyperbola with intercept at (8,0) and focus at (11,0)
7. Evaluate the determinant | 2 3 4 |
| 0 5 1 |
| 6 0 7 |
8. Find the area of a triangle with coordinates A(2,5) B( 7,2) and C( 4, 8)
9. Solve by Cramer rule
A. 4x β 7y = 11 D= Dx= Dy =
5x + 7y = 3 x = y =
B. 4x β 3y +2z = 25 D= Dx= Dy = Dz=
x + y β z = 4 x = y = z =
3x + 2y β 5z = 4
10. Solve each non-linear system
A. y = βπ₯ β 1 and y= x β 3
B. y= x2
-7x +5 and y = 2x β 3
C. y= 3×2 +x β 5 and y = 2×2 βx β 2
D. x
2 β y
2 = 4 and 3×2 + y2 = 16
11. Find the fraction decomposition
A. π€π₯+2
π₯
2β3π₯β4

B. 2π₯+5
π₯
3+3π₯
2

C. π₯+1
π₯(π₯+1)2

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