Kreistangenten Normalvektorform Spaltform 2
Ermittle die Gleichung der Tangente im vorgegebenen Punkt:
k: x² + y² – 4x + 6y – 87 = 0 T (- 4/ yT > 0)
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1. Wir ermitteln den Punkt T:
k: x² – 4x + 4 + y² + 6y + 9 – 87 = 87 + 4 + 9
k: (x – 2)² + (y + 3)² = 100
d.f. k: M (2/-3) r = 10
(- 4 – 2)² + (y + 3)² = 100
36 + (y + 3)² = 100 / – 36
(y + 3)² = 64 / √
y = – 3 +/- 8 d.f. y = 5 (da yT> 0)
d.f. T (-4/5)
2. Normalvektorform:
(T – M) * (X – T) = 0
d.f. (- 4 – 2) * (x + 4) = 0
(5 + 3) * (y – 5) = 0
– 6 * (x + 4) = 0
8 * (y – 5) = 0
-6x – 24 = 0
8y – 40 = 0
– 6x + 8y – 64 = 0 / + 64
d.f. -6x + 8y = 64
3. Spaltform:
(T – M) * (X – M) = r²
(- 4 – 2) * (x – 2) + (5 + 3) * (y + 3) = 100
– 6 * (x – 2) + 8 (y + 3) = 100
– 6x + 12 + 8y + 24 = 100
– 6x + 8y + 36 = 100 / – 36
d.f. -6x + 8y = 64