APPLY – Topic 15.1

Homework Assignment

1. Write the equation in standard form of the circle whose

center is at (0, 0) that passes through the point (5, 12).

2. Write the equation in standard form of the circle whose

center is at (-4, -2) that passes through the point (1, 10).

3. Find the equation in standard form of the parabola that

open to the right, has it vertex at (5, 0), and goes through

the point (10, ).

4. Find the equation in standard form of the parabola that

opens downward, has it vertex at (2, -1), and goes through

the point (10, -9).

5. Find the equation in standard form of the parabola that

opens to the left, has its vertex at (5, -4), and goes through

the point (2, 2).

6. Graph the circle whose equation is x² + y² = 44.

7. Graph the circle whose equation is

                                            (x + 2)² + (y - 3)² = 121.

8. Graph the circle whose equation is

                                              x² + y² + 12x - 6y = 4.

9. Graph the parabola whose equation is (y - 2)² = 12(x - 1).

10. Graph the parabola whose equation is

                                               x² - 10x - 12y = -37

11. Find the standard form for the equation of the ellipse

whose center is at (0, 0), whose major axis, of length 14,

is along the y-axis, and whose minor axis of length 8.

12. Find the standard form for the equation of the ellipse

whose center is at (0, 0), whose major axis, of length 12, is

along the x-axis, and whose minor axis intersects the ellipse

at the point (0, 3).

13. Find the standard form for the equation of the ellipse whose

center is at (2, -7), whose major axis, of length 52, is parallel

to the y-axis, and which has a focus at (2, 17).

14. Find the standard form for the equation of the ellipse whose

vertices are at (3, 2) and (-7, 2) and whose minor axis is of

length 6.

15. Find the standard form for the equation of the ellipse whose

center is at (5, -5), whose major axis is of length 10, and

which passes through the point (5, -2).

16. Graph the ellipse whose equation is .

17. Graph the ellipse whose equation is .

18. Graph the ellipse whose equation is .

19. Graph the ellipse whose equation is .

20. Graph the ellipse whose equation is

                                                   9x² + 4y² - 36x + 32y = 44.

21. Find the standard form for the equation of the hyperbola

whose center is at (0, 0), which has vertices at the points

(-2, 0) and (2, 0), and which passes through the point (3, 5).

22. Find the standard form for the equation of the hyperbola

whose center is at (0, 0), which has vertices at the points

(0, -6) and (0, 6), and which passes through the point

(4, 10).

23. Find the standard form for the equation of the hyperbola

whose center is at (0, 0), whose transverse axis, of length

24, is along the x-axis, and which has a focus at (13, 0).

24. Find the standard form for the equation of the hyperbola

whose center is at (4, -2), which has vertices at the points

(4, 3) and (4, -7), and which passes through the point

(-4, 13).

25. Graph the hyperbola whose equation is .

26. Graph the hyperbola whose equation is .

27. Graph the hyperbola whose equation is

                                                  -81x² + 36y² = 324.

28. Graph the hyperbola whose equation is

                                              .

29. Graph the hyperbola whose equation is

                                              .

30. Graph the hyperbola whose equation is

                                -9x² + y² + 90x + 8y = 245.