achse 9x^2+9y^2+18x-18y+14=0

Lösung

achse

9 x^{2} + 9 y^{2} + 18 x - 18 y + 14 = 0

semi - major axis b = \frac{2}{3}, semi - minor axis a = \frac{2}{3}

Schritte zur Lösung

9 x^{2} + 9 y^{2} + 18 x - 18 y + 14 = 0

Rewrite

9 x^{2} + 9 y^{2} + 18 x - 18 y + 14 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 1, 1), a = \frac{2}{3}, b = \frac{2}{3}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 1, 1), b = \frac{2}{3}, a = \frac{2}{3}

a x i s \frac{x ^{2}}{49} + \frac{y ^{2}}{9} = 1

a x i s \frac{x ^{2}}{8} + \frac{y ^{2}}{3} = 1

a x i s \frac{x ^{2}}{36} + \frac{y ^{2}}{4} = 1

a x i s \frac{x ^{2}}{63500} + \frac{y ^{2}}{50900} = 1

a x i s 25 x^{2} + 9 y^{2} = 225