foki 16x^2+4y^2+96x-24y+116=0

Lösung

foki

16 x^{2} + 4 y^{2} + 96 x - 24 y + 116 = 0

(- 3, 3 + 23), (- 3, 3 - 23)

Schritte zur Lösung

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

Calculate ellipse properties

16 x^{2} + 4 y^{2} + 96 x - 24 y + 116 = 0 :

Ellipse with center

(h, k) = (- 3, 3), b = 4, a = 2

(- 3, 3 + c), (- 3, 3 - c)

Compute

c :

c = 4^{2} - 2^{2} : 23

(- 3, 3 + 23), (- 3, 3 - 23)

f oc i \frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1

ce n t er \frac{x ^{2}}{9} + \frac{y ^{2}}{25} = 1

ce n t er \frac{x ^{2}}{25} + \frac{( y + 3 ) ^{2}}{49} = 1

ce n t er 3 x^{2} + y^{2} - 24 x + 39 = 0

ce n t er \frac{( x - 3 ) ^{2}}{49} + \frac{( y + 5 ) ^{2}}{25} = 1