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Pre Calculus

Systems of Conic Sections Notes

Name___________________________________

Date________________ Period____

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-1-

State if the point given is a solution to the system of equations.

1) 3y2 + 13x + 6y - 137 = 015x2 - 3y2 - 28x - 6y - 163 = 0Point: (7, -4)

2) x2 - 3y2 + 30x + 2y - 192 = 0x + y - 2 = 0Point: (10, -8)

Solve each system of equations.

3) 2y2 - 27x - 3y + 180 = 0x + y = 4

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-2-

4) 2x2 - 3y2 + 76x + 4y + 4 = 03x + y = 2

5) 2x2 - y2 + 4x + 10y - 32 = 014x2 - y2 + 28x + 10y - 128 = 0

6) 4x2 - 2y2 - 55x + 20y + 138 = 0-9x2 + 2y2 + 53x - 20y - 151 = 0

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-3-

Write the equation of each conic section in standard form.

7) 4x2 + 25y2 + 8x - 250y + 529 = 0 8) 6y2 + x + 36y + 57 = 0

9) 2y2 - 12x = -12y - 2x2 - 28 10) 4x - 6 = y2 - x2 - 2y

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-4-

Answers to Systems of Conic Sections Notes

1) No 2) Yes 3) (10, -6) 4) (0, 2), (4, -10)5) (-4, 8), (-4, 2), (2, 8), (2, 2) 6) No solution.

7) (x + 1)2

25 +

(y - 5)2

4 = 1

8) x = -6(y + 3)2 - 3 9) (x - 3)2

+ (y + 3)2 = 4

10) (x + 2)2

9 -

(y - 1)2

9 = 1