foki (x^2)/(81/4)+(y^2)/(25/16)=1

Lösung

foki

\frac{x ^{2}}{\frac{81}{4}} + \frac{y ^{2}}{\frac{25}{16}} = 1

(\frac{299}{4}, 0), (- \frac{299}{4}, 0)

Schritte zur Lösung

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

Calculate ellipse properties

\frac{x ^{2}}{\frac{81}{4}} + \frac{y ^{2}}{\frac{25}{16}} = 1 :

Ellipse with center

(h, k) = (0, 0), a = \frac{9}{2}, b = \frac{5}{4}

(0 + c, 0), (0 - c, 0)

Compute

c :

c = (\frac{9}{2})^{2} - (\frac{5}{4})^{2} : \frac{299}{4}

(0 + \frac{299}{4}, 0), (0 - \frac{299}{4}, 0)

Fasse zusammen

(\frac{299}{4}, 0), (- \frac{299}{4}, 0)

f oc i \frac{( y - 1 ) ^{2}}{4} + \frac{( x ^{2} )}{25} = 1

f oc i x^{2} + 4 y^{2} - 4 x - 8 y - 92 = 0

f oc i x^{2} + 9 y^{2} = 36

f oc i 8 x^{2} + 4 y^{2} + 16 x - 12 y - 15 = 0

f oc i 9 x^{2} + 16 y^{2} = 1