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

Lösung

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

(h, k) = (4, - 2), a = 2, b = 3

Schritte zur Lösung

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (4, - 2), a = 2, b = 3

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (4, - 2), b = 3, a = 2

\frac{x ^{2}}{4} + \frac{y ^{2}}{4 - 16} = 1

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

3 x^{2} + 4 y^{2} - 18 x - 8 y - 17 = 0

\frac{x ^{2}}{20} + \frac{y ^{2}}{16} = 1

\frac{( x + 7 ) ^{2}}{16} + \frac{( y - 4 ) ^{2}}{25} = 1