Instructions:Answer all the following questions in the space provided. Simplify all answers.
- What effect can the xy term have on the general conic sections?
- What is the locus definition of an ellipse? Define the terms used in the definition. (You may use a diagram to help explain.)
- Given the following ellipses, find their focal points.
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| c) | (x + 1)2
36 | + | (y - 4)2
11 | = 1 |
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| d) | (x - 2)2
16 | + | (y + 3)2
36 | = 1 |
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- For the following pairs of focal points, find the standard equation of each ellipse.
a) (-2, 0) and (2, 0) and 2a = 6
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b) (0, 3) and (0, -3) and 2b = 10
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c) (1, 1) and (-1, 1) and 2a = 4
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- What is the locus definition of a hyperbola? Define the terms used in the definition. (You may use a diagram to help explain.)
- Given the following hyperbolas, find their foci and vertices.
- For the following pairs of focal points and vertices, find the standard equation of each hyperbola.
| a) | foci: (3, 0) and (-3, 0) |
| vertices: (1, 0) and (-1, 0)
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| b) | foci: (0, 5) and (0, -5) |
| vertices: (0, 2) and (0, -2)
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| c) | foci: (6, 0) and (-6, 0) |
| vertices: (2, 0) and (-2, 0)
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- What is the locus definition of a parabola? Define the terms used in the definition. (You may use a diagram to help explain.)
- Given the equation of each parabola, find the focal point and the equation of the directrix.
a) y = x2 + 2x + 1
b) y2 - 8x + 2y + 17 = 0
c) 2y2 + 8y - 16x = 8
d) 2x2 - 5x - y + 4 = 0
- Given the following focal points, vertices and directrixes, find the standard equation of each parabola.
| a) | focus: (0, 0) |
| vertex: (0, -2) |
| directrix: y = -4
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| b) | focus: (2, 3) |
| vertex: (5, 3) |
| directrix: x = 8
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