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

Lösung

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

(h, k) = (- 1, 2), a = 6, b = 3

Schritte zur Lösung

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - ( - 1 ) ) ^{2}}{6 ^{2}} + \frac{( y - 2 ) ^{2}}{3 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 1, 2), a = 6, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 1, 2), a = 6, b = 3

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

\frac{x ^{2}}{36} + \frac{y ^{2}}{2. 5 ^{2}} = 1

x^{2} + y^{2} = 3 y

2 x^{2} + 5 y^{2} = 10

x^{2} + 9 y^{2} + 8 x - 36 y + 43 = 0