For Exercises 43–56, write the standard form of an equation of an ellipse subject to the given conditions. (See Example 5) Vertices: ( 6 , 0 ) and ( − 6 , 0 ) ; Foci: ( 5 , 0 ) and ( − 5 , 0 )
For Exercises 43–56, write the standard form of an equation of an ellipse subject to the given conditions. (See Example 5) Vertices: ( 6 , 0 ) and ( − 6 , 0 ) ; Foci: ( 5 , 0 ) and ( − 5 , 0 )
Solution Summary: The author calculates the equation of ellipse in standard form whose vertices are (6,0)and
In Exercises 35–42, find the vertex, focus, and directrix of each
parabola with the given equation. Then graph the parabola.
35. (x – 2) = 8(y – 1)
37. (x + 1) = -8(y + 1)
39. (y + 3) = 12(x + 1)
41. (y + 1) = -&r
36. (x + 2) = 4(y + 1)
38. (x + 2) = -8(y + 2)
40. (y + 4)2 = 12(x + 2)
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42. (y - 1) = -&r
For Exercises 43–48, the equation represents a conic section (nondegenerative case).
a. Identify the type of conic section. (See Example 6)
b. Graph the equation on a graphing utility.
43. 4x – 4xy + 5y – 20 = 0
44. 6x + 4V3xy + 2y - 18x + 18V3y – 72 = 0
45. 2x – 6xy + 3y²
- 4x + 12y – 9 = 0
46. 5x – 3xy + 2y – 6 = 0
47. 4x + 8xy + 4y – 2x – 5y – 2 = 0
48. 4x? + 8V3xy + 3y + 2x – 12y – 6 = 0
Exercises 98–100 will help you prepare for the material covered
in the first section of the next chapter.
98. a. Does (-5, –6) satisfy 2x – y = -4?
b. Does (-5, -6) satisfy 3x – 5y = 15?
99. Graph y = -x – 1 and 4x – 3y = 24 in the same
rectangular coordinate system. At what point do the graphs
intersect?
100. Solve: 7x – 2(-2x + 4) = 3.
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