Conics Worksheet With Answers Page 2
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8Conics Lesson 6
Part I: General Form
+ Dx + Ey + F = 0
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General Form of a Conic: Ax
+ Cy
A & C are useful in finding out which conic is produced:
A = C Circle
AC > 0 Ellipse
A or C = 0 Parabola
AC < 0 Hyperbola
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Example 1: What shape is the graph of 3x
– 2y
+ 2x - 3 = 0
Hyperbola, since AC = (3)(-2) = -6, which is negative.
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Example 2: What shape is the graph of y
+ 2x - y - 5 = 0
Parabola, since A = 0
Questions:
Based on the A & C values, determine the type of conic
for each of the following:
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1) 9x
- 4y
- 8y + 32 = 0
Why is there
no B?
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2) -2y
- x + 20y - 47 = 0
B
The
xy term
involves conic
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3) y
+ 6y = 3x - 12
rotation, and is
excluded from
the Pure Math 30
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4) 25x
- 9y
- 72y - 100x - 269 = 0
curriculum.
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5) 4x
+ y
- 8x + 4y - 9 = 0
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Answers:
6) 9x
- 4y
- 40y - 136 = 0
1) Hyperbola
2) Parabola
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7) x
+ 6x + 8y + 33 = 0
3) Parabola
4) Hyperbola
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8) 4x
+ 4y
- 8x + 4y - 9 = 0
5) Ellipse
6) Hyperbola
7) Parabola
8) Circle
Pure Math 30: Explained!
106
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