achse ((x-3)^2)/9+((y+1)^2)/4 =1

Lösung

achse

\frac{( x - 3 ) ^{2}}{9} + \frac{( y + 1 ) ^{2}}{4} = 1

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

Schritte zur Lösung

\frac{( x - 3 ) ^{2}}{9} + \frac{( y + 1 ) ^{2}}{4} = 1

Rewrite

\frac{( x - 3 ) ^{2}}{9} + \frac{( y + 1 ) ^{2}}{4} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

a x i s (\frac{x - 1}{25})^{2} + (\frac{y - 3}{16})^{2} = 1

a x i s \frac{( x + 1 ) ^{2}}{64} + \frac{( y - 6 ) ^{2}}{16} = 1

a x i s \frac{x ^{2}}{144} + \frac{y ^{2}}{81} = 1

a x i s 16 x^{2} - 64 x + 9 y^{2} - 54 y = - 1

a x i s 4 x^{2} + 9 y^{2} - 64 x + 54 y + 301 = 0