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

Lösung

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

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

Schritte zur Lösung

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

y = 4 (x^{2} + y^{2})

4 x^{2} + 3 y^{2} + 8 x - 6 y - 41 = 0

x^{2} + 4 y^{2} + 4 y = 3

49 x^{2} + 16 y^{2} + 196 x - 96 y = 444

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