((x-2)^2)/9+((y+4)^2)/(16)=1

Lösung

\frac{( x - 2 ) ^{2}}{9} + \frac{( y + 4 ) ^{2}}{16} = 1

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

Schritte zur Lösung

\frac{( x - 2 ) ^{2}}{9} + \frac{( y + 4 ) ^{2}}{16} = 1

Rewrite

\frac{( x - 2 ) ^{2}}{9} + \frac{( y + 4 ) ^{2}}{16} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

(x - 1)^{2} + (2 y + 4)^{2} = 16

64 xx - 256 x + 81 yy + 810 y = 2903

9 x^{2} + 36 y^{2} + 36 x - 216 y + 36 = 0

25 x^{2} + 16 y^{2} - 400 = 0

4 x^{2} + 9 y^{2} - 24 x - 36 y + 36 = 0