Pre calculus test

MAC 1147 TEST 4 ____________________

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1. Find focus, directrix, and graph y2 = 7 x

2. Write the equation of the parabola given vertex at (0,0) and directrix at y = -2.

3. Write the equation of a parabola given focus at ( 0,9) and directrix at y= -9.

4. Find focus, vertices, and graph 𝑥 2

100 +

𝑦2

36 = 1

5. Find the focus of the graph 𝑥 2

15 +

𝑦2

35 = 1

6. Write the equation of an ellipse with focus at (0,7) and vertices at (0,10), centered at

(0,0).

7. Write the equation of an ellipse with x-intercepts of (±6,0) and y-intercepts of (0,±2)

8. Find focus, vertices, asymptotes, and graph hyperbola 𝑥 2

25 −

𝑦2

4 = 1

9. Find the equation of a hyperbola with intercept at (5,,0) and focus at (2√3,0)

10. Find the asymptotes of the hyperbola given intercept at (0,4) and focus at (0, 3√2)

11. Find the area of a triangle with coordinates A(0,4) B( 0,6) and C( 8,10)

12. Solve by Cramer rule

A. 5x + 2y = 13 D= Dx= Dy =

7x + 9y = 7 x = y =

B. 4x – 3y +z = 15 D= Dx= Dy = Dz=

2x +4 y – z = 8 x = y = z =

x + y + 2z = 10

13. Solve each non-linear system for x

A. y = √𝑥 + 3 and y= x – 3

B. y= x2 +2 and y= - x2 -3x +3

C. 2x2 + y2 = 16 and 4x2 + y2 = 32

14. Find the fraction decomposition [ 2 points each]

A. 3𝑥 +4

𝑥 2+4𝑥 −5

C. 5𝑥 −6

𝑥 3−4𝑥

B. 2𝑥 +1

𝑥(𝑥−4)2