For Exercises 59–64, use the standard form of a parabola given by y = a x 2 + b x + c to write an equation of a parabola that passes through the given points. (See Example 5.) ( 2 , 1 ) , ( − 2 , 5 ) , and ( 1 , − 4 )
For Exercises 59–64, use the standard form of a parabola given by y = a x 2 + b x + c to write an equation of a parabola that passes through the given points. (See Example 5.) ( 2 , 1 ) , ( − 2 , 5 ) , and ( 1 , − 4 )
Solution Summary: The author calculates the equation of the parabola which passes through the given points (2,1),.
For Exercises 59–64, use the standard form of a parabola given by
y
=
a
x
2
+
b
x
+
c
to write an equation of a parabola that passes through the given points. (See Example 5.)
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)
%3D
%3D
42. (y - 1) = -&r
In Exercises 5–12, find the standard form of the equation of each
hyperbola satisfying the given conditions.
5. Foci: (0, –3), (0, 3); vertices: (0, –1), (0, 1)
6. Foci: (0, –6), (0, 6); vertices: (0, -2), (0, 2)
7. Foci: (-4, 0), (4, 0); vertices: (-3, 0), (3,0)
8. Foci: (-7, 0), (7, 0); vertices: (-5, 0), (5,0)
9. Endpoints of transverse axis: (0, -6), (0, 6); asymptote:
y = 2x
10. Endpoints of transverse axis: (-4,0), (4, 0); asymptote:
y = 2r
11. Center: (4, -2); Focus: (7, -2); vertex: (6, -2)
12. Center: (-2, 1); Focus: (-2, 6); vertex: (-2, 4)
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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