Ergebnisse: Kegelschnitte

1. 1. 9x² + 25y² = 225
   2. x² + 16y² = 400
   3. 9x² + 25y² = 900
   4. x² + 2y² = 16
   5. x² + 5y² = 125
   6. 4x² + 9y² = 900
   7. 16x² - 9y² = 144
   8. x² - y² = 25
   9. 9x² - 16y² = 144
   10. 5x² - 4y² = 80
   11. 16x² - 9y² = 576
   12. x² - 2y² = 54
   13. y² = 4x
   14. y² = 12x
2. 1. a = 5, b = 4, e = 3
   2. a = 10, b = 5, e = 5√3
   3. a = 9, b = 6, e = 3√5
   4. a = 6, b = 2√5, e = 4
   5. a = 15, b = 5, e = 5√10
   6. a = 10, b = 10, e = 10√2
   7. a = 6, b = 4, e = 2√13
   8. a = 2, b = 2√3, e = 4
   9. p = 4, e = 2
   10. p = 1/2, e = 1/4
3. 1. x² + 4y² = 100
   2. x² + 16y² = 400
   3. 4x² + 9y² = 900
   4. x² + 25y² = 50
   5. x² - 5y² = 100
   6. 25x² - 4y² = 900
   7. x² - 9y² = 144
   8. x² - y² = 36
   9. y² = 8x
   10. y² = 3x/2
4. 1. S₁(-4/-1), S₂(2/2)
   2. -
   3. S₁(40/15), S₂(48/7)
   4. T(4/1,8)
   5. S₁(-3/0), S₂(5/-4)
   6. S₁(3/3), S₂(4/5)
   7. T(7,5/3)
   8. -
   9. S₁(4/4), S₂(9/6)
   10. S₁(4/-1), S₂(9/1,5)
   11. -
   12. T(2,25/4,5)
5. 1. 3x + 8y = 50
   2. -x + 2y = 8
   3. 4x - 5y = 25
   4. 5x - 4y = 9
   5. 2x + y = 1
   6. -13x + 24y = 25
   7. y = x + 2
   8. y = -x/4 - 3
6. 1. ell: a = √18, b = √2; k: r = √10
      S_1-4(±3/±1), φ = 53,1°
   2. hyp: a = √3, b = √12; k: r = √8
      S_1-4(±2/±2), φ = 59,0°
   3. hyp: a = 16, b = 8; ell: a = 25, b = 10
      S_1-4(±20/±6), φ = 112,1°
   4. ell: a = 15, b = 5; k: M(16/0), r = 5
      S_1,2(12/±3), φ = 77,1°
   5. par: p = 1; hyp: a = √3, b = √12
      S_1,2(2/±2), φ = 49,4°
   6. par: p = 1/2; ell: a = 4√2, b = 2√2
      S_1,2(4/±2), φ = 139,4°

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