achse ((x-5)^2)/9+((y-3)^2)/(16)=1

Lösung

achse

\frac{( x - 5 ) ^{2}}{9} + \frac{( y - 3 ) ^{2}}{16} = 1

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

Schritte zur Lösung

\frac{( x - 5 ) ^{2}}{9} + \frac{( y - 3 ) ^{2}}{16} = 1

Rewrite

\frac{( x - 5 ) ^{2}}{9} + \frac{( y - 3 ) ^{2}}{16} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

a x i s x^{2} + 4 y^{2} = 25

a x i s 4 x^{2} + 9 y^{2} - 8 x - 36 y + 4 = 0

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

a x i s 3 x^{2} + 4 y^{2} + 27 x - 16 y + 48 = 0

a x i s x^{2} + y^{2} + 10 x - 8 y = - 32