22x^2+66y^2+60x+4y+9=0

Lösung

22 x^{2} + 66 y^{2} + 60 x + 4 y + 9 = 0

(h, k) = (- \frac{15}{11}, - \frac{1}{33}), a = \frac{1055}{11 6}, b = \frac{1055}{33 2}

Schritte zur Lösung

22 x^{2} + 66 y^{2} + 60 x + 4 y + 9 = 0

Rewrite

22 x^{2} + 66 y^{2} + 60 x + 4 y + 9 = 0

in the form of the standard ellipse equation

\frac{( x - ( - \frac{15}{11} ) ) ^{2}}{( \frac{1055}{11 6} ) ^{2}} + \frac{( y - ( - \frac{1}{33} ) ) ^{2}}{( \frac{1055}{33 2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- \frac{15}{11}, - \frac{1}{33}), a = \frac{1055}{11 6}, b = \frac{1055}{33 2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- \frac{15}{11}, - \frac{1}{33}), a = \frac{1055}{11 6}, b = \frac{1055}{33 2}

2 x^{2} + 2 y^{2} + 36 y = 0

64 x^{2} + 81 y^{2} - 1152 x - 486 y + 729 = 0

4 = x^{2} + 4 y^{2}

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

\frac{x ^{2}}{28} + \frac{y ^{2}}{64} = 1