College Algebra, 4th Edition

Review Exercises

In Exercises 1–8, sketch the graph of each parabola. Determine the vertex, focus, axis, and directrix of each parabola.

1. $y^2=-6x$

2. $y^2=12x$

3. $x^2=7y$

4. $x^2=-3y$

5. ${(x-2)}^2=-(y+3)$

6. ${(y+1)}^2=5(x+2)$

7. $y^2=-4y+2x+1$

8. $-x^2+2x+y=0$

In Exercises 9–12, find an equation of the parabola satisfying the given conditions.

9. Vertex: (0, 0) focus: $(-3,0)$

10. Vertex: (0, 0) focus: (0, 4)

11. Focus: (0, 4) directrix: $y=-4$

12. Focus: $(-3,0);$ directrix: $x=3$

In Exercises 13–20, sketch the graph of each ellipse. Determine the foci, vertices, and endpoints of the minor axis of the ellipse.

13. ${\displaystyle \frac{x^2}{25}}+{\displaystyle \frac{y^2}{4}}=1$

14. ${\displaystyle \frac{x^2}{9}}+{\displaystyle \frac{y^2}{36}}=1$

     

15. $4x^2+y^2=4$

16. $16x^2+y^2=64$

17. $16{(x+1)}^2+9{(y+4)}^2=144$

18. $4{(x-1)}^2+3{(y+2)}^2=12$

19. $x^2+9y^2+2x-18y+1=0$

20. $4x^2+y^2+8x-10y+13=0$

In Exercises 21–24, find an equation of the ellipse satisfying the given conditions. ...