((x-3)^2)/(225)+((y+9)^2)/(121)=1

Lösung

\frac{( x - 3 ) ^{2}}{225} + \frac{( y + 9 ) ^{2}}{121} = 1

(h, k) = (3, - 9), a = 15, b = 11

Schritte zur Lösung

\frac{( x - 3 ) ^{2}}{225} + \frac{( y + 9 ) ^{2}}{121} = 1

Rewrite

\frac{( x - 3 ) ^{2}}{225} + \frac{( y + 9 ) ^{2}}{121} = 1

in the form of the standard ellipse equation

\frac{( x - 3 ) ^{2}}{1 5 ^{2}} + \frac{( y - ( - 9 ) ) ^{2}}{1 1 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (3, - 9), a = 15, b = 11

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (3, - 9), a = 15, b = 11

\frac{x ^{2}}{15} + \frac{y ^{2}}{45} = 1

\frac{( x + 11 ) ^{2}}{100} + \frac{( y - 4 ) ^{2}}{1 9 ^{2}} = 1

100 x^{2} + 9 y^{2} = 900

25 x^{2} + 4 y^{2} - 225 = 0

16 x^{2} + 36 y^{2} - 224 x + 208 = 0