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.) ( 1 , 4 ) , ( − 1 , 6 ) , and ( 2 , 18 )
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.) ( 1 , 4 ) , ( − 1 , 6 ) , and ( 2 , 18 )
Solution Summary: The author calculates the equation of the parabola which passes through the given points (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.)
In Exercises 3–10, describe the curve represented by each equation.
Identify the type of curve and its center (or vertex if it is a parabola).
Sketch each curve.
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)
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