achse ((x+5)^2)/9+((y+1)^2)/4 =1

Lösung

achse

\frac{( x + 5 ) ^{2}}{9} + \frac{( y + 1 ) ^{2}}{4} = 1

semi - major axis a = 3, semi - minor axis b = 2

Schritte zur Lösung

\frac{( x + 5 ) ^{2}}{9} + \frac{( y + 1 ) ^{2}}{4} = 1

Rewrite

\frac{( x + 5 ) ^{2}}{9} + \frac{( y + 1 ) ^{2}}{4} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 5, - 1), a = 3, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 5, - 1), a = 3, b = 2

a x i s 2 x^{2} + 3 y^{2} = 4

a x i s \frac{( x - 4 ) ^{2}}{64} + \frac{( y - 2 ) ^{2}}{39} = 1

a x i s \frac{( x - 1 ) ^{2}}{13} + \frac{( y + 5 ) ^{2}}{12} = 1

a x i s \frac{( x + 8 ) ^{2}}{64} + \frac{( y - 11 ) ^{2}}{36} = 1

a x i s 5 x^{2} + 20 y^{2} = 50