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

Lösung

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

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

Schritte zur Lösung

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

25 x^{2} + 16 y^{2} - 100 x - 96 y - 156 = 0

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

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

16 - x^{2} - 4 y^{2} > 0

9 x^{2} + 4 y^{2} - 54 x - 8 y - 59 = 0