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Locus

The Circle

The Ellipse

The Parabola

The Hyperbola

General Form

Intersections of Lines & Conics

Summary&Test

 

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Unit 9 : THE CONICS

LESSON 8: UNIT TEST

 

1. Determine the type of conic in each case by completing the chart.

 

Conic in general form

Value of a

Value of b

Condition on a, b

Type of Conic

5x2 - 2y2 + x + 2y 16 = 0

 

 

 

 

x2 + y2 2x y 12 = 0

 

 

 

 

y2 4x 6y 9 = 0

 

 

 

 

9x2 + y2 6y + 8x 2 = 0

 

 

 

 

x2 6x 3y 6 = 0

 

 

 

 

 

 

 

 

 

 

 

 

Solutions:

1. Determine the type of conic in each case by completing the chart.

 

Conic in general form

Value of a

Value of b

Condition on a, b

Type of Conic

5x2 - 2y2 + x + 2y 16 = 0

5

-2

ab < 0

Hyperbola

x2 + y2 2x y 12 = 0

1

1

ab = 1

Circle

y2 4x 6y 9 = 0

0

1

ab = 0

Parabola

9x2 + y2 6y + 8x 2 = 0

9

1

ab > 0

Ellipse

x2 6x 3y 6 = 0

1

0

ab = 0

Parabola

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


 

 


 

 

 

 

 

 

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