foki 4x^2+9y^2+12x-108y+297=0

Lösung

foki

4 x^{2} + 9 y^{2} + 12 x - 108 y + 297 = 0

(\frac{- 3 + 2 5}{2}, 6), (\frac{- 3 - 2 5}{2}, 6)

Schritte zur Lösung

(h + c, k), (h - c, k)

Calculate ellipse properties

4 x^{2} + 9 y^{2} + 12 x - 108 y + 297 = 0 :

Ellipse with center

(h, k) = (- \frac{3}{2}, 6), a = 3, b = 2

(- \frac{3}{2} + c, 6), (- \frac{3}{2} - c, 6)

Compute

c :

c = 3^{2} - 2^{2} : 5

(- \frac{3}{2} + 5, 6), (- \frac{3}{2} - 5, 6)

Fasse zusammen

(\frac{- 3 + 2 5}{2}, 6), (\frac{- 3 - 2 5}{2}, 6)

f oc i 3 x^{2} + 4 y^{2} = 48

f oc i \frac{x ^{2}}{4} + \frac{y ^{2}}{20} = 1

f oc i \frac{( x 8 ) ^{2}}{49} + \frac{( y + 1 ) ^{2}}{100} = 1

f oc i 9 x^{2} + 49 y^{2} + 18 x + 294 y - 9 = 0

f oc i 16 x^{2} + 64 y^{2} = 128