achse ((x-1)^2)/9+((y+5)^2)/(16)=1

Lösung

achse

\frac{( x - 1 ) ^{2}}{9} + \frac{( y + 5 ) ^{2}}{16} = 1

semi - major axis b = 4, semi - minor axis a = 3

Schritte zur Lösung

\frac{( x - 1 ) ^{2}}{9} + \frac{( y + 5 ) ^{2}}{16} = 1

Rewrite

\frac{( x - 1 ) ^{2}}{9} + \frac{( y + 5 ) ^{2}}{16} = 1

in the form of the standard ellipse equation

\frac{( x - 1 ) ^{2}}{3 ^{2}} + \frac{( y - ( - 5 ) ) ^{2}}{4 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (1, - 5), a = 3, b = 4

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (1, - 5), b = 4, a = 3

a x i s \frac{( y + 4 ) ^{2}}{9} + \frac{( x - 9 ) ^{2}}{25} = 1

a x i s 25 x^{2} + 16 y^{2} = 400

a x i s 9 x^{2} + 4 y^{2} + 18 x - 8 y - 131 = 0

a x i s \frac{( x - 1 ) ^{2}}{6} + \frac{( y - 3 ) ^{2}}{2} = 1

a x i s \frac{x ^{2}}{64} + \frac{y ^{2}}{100} = 1