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Unit 10 : THE CONICS
LESSON 8: UNIT TEST
1. Determine the type of conic in each case by completing the chart.
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Conic in general form |
Value of “a” |
Value of “b” |
Condition on a, b |
Type of Conic |
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5x2 - 2y2 + x + 2y – 16 = 0 |
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x2 + y2 – 2x –y –12 = 0 |
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y2 – 4x – 6y – 9 = 0 |
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9x2 + y2 – 6y + 8x – 2 = 0 |
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x2 – 6x – 3y – 6 = 0 |
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Solutions:
1. Determine the type of conic in each case by completing the chart.
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Conic in general form |
Value of “a” |
Value of “b” |
Condition on a, b |
Type of Conic |
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5x2 - 2y2 + x + 2y – 16 = 0 |
5 |
-2 |
ab < 0 |
Hyperbola |
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x2 + y2 – 2x –y –12 = 0 |
1 |
1 |
ab = 1 |
Circle |
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y2 – 4x – 6y – 9 = 0 |
0 |
1 |
ab = 0 |
Parabola |
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9x2 + y2 – 6y + 8x – 2 = 0 |
9 |
1 |
ab > 0 |
Ellipse |
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x2 – 6x – 3y – 6 = 0 |
1 |
0 |
ab = 0 |
Parabola |
