achse 16x^2+9y^2-128x-18y+121=0

Lösung

achse

16 x^{2} + 9 y^{2} - 128 x - 18 y + 121 = 0

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

Schritte zur Lösung

16 x^{2} + 9 y^{2} - 128 x - 18 y + 121 = 0

Rewrite

16 x^{2} + 9 y^{2} - 128 x - 18 y + 121 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

a x i s 4 x^{2} + y^{2} + 16 x + 4 y + 4 = 0

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

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

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

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