achse (x^2)/(5^2)+(y^2)/(13^2)=1

Lösung

achse

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

semi - major axis b = 13, semi - minor axis a = 5

Schritte zur Lösung

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{5 ^{2}} + \frac{( y - 0 ) ^{2}}{1 3 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 5, b = 13

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 13, a = 5

a x i s 16 x^{2} + 9 y^{2} - 144 = 0

a x i s \frac{( x - 5 ) ^{2}}{49} + \frac{( y - 9 ) ^{2}}{25} = 1

a x i s \frac{x ^{2}}{56} + \frac{y ^{2}}{36} = 1

a x i s 25 x^{2} + 16 y^{2} + 100 x + 96 y - 156 = 0

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