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

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 π‘₯2

100 +

𝑦2

36 = 1

5. Find the focus of the graph π‘₯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 (Β±6,0) and y-intercepts of (0,Β±2)

8. Find focus, vertices, asymptotes, and graph hyperbola π‘₯2

25 βˆ’

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 = √π‘₯ + 3 and y= x – 3

B. y= x2 +2 and y= – x2 -3x +3

C. 2×2 + y2 = 16 and 4×2 + y2 = 32

14. Find the fraction decomposition [ 2 points each]

A. 3π‘₯+4

π‘₯2+4π‘₯βˆ’5

C. 5π‘₯βˆ’6

π‘₯3βˆ’4π‘₯

B. 2π‘₯+1

π‘₯(π‘₯βˆ’4)2