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

Lösung

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

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

Schritte zur Lösung

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

49 x^{2} + 4 y^{2} = 196

18 y^{2} + 24 y + 12 x^{2} - 12 x = 1

x^{2} + 2 y^{2} - 2 x - 4 y = - 1

\frac{x ^{2}}{7 ^{2}} + \frac{y ^{2}}{3 ^{2}} = 1

16 x^{2} + 25 y^{2} - 64 x + 150 y = - 279