((x+3)^2)/9+((y-1)^2)/(25)-1=0

Lösung

\frac{( x + 3 ) ^{2}}{9} + \frac{( y - 1 ) ^{2}}{25} - 1 = 0

(h, k) = (- 3, 1), a = 3, b = 5

Schritte zur Lösung

\frac{( x + 3 ) ^{2}}{9} + \frac{( y - 1 ) ^{2}}{25} - 1 = 0

Rewrite

\frac{( x + 3 ) ^{2}}{9} + \frac{( y - 1 ) ^{2}}{25} - 1 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 3 ) ) ^{2}}{3 ^{2}} + \frac{( y - 1 ) ^{2}}{5 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 3, 1), a = 3, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 3, 1), b = 5, a = 3

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

\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