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{1649}{11 6}, b = \frac{1649}{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{1649}{11 6} ) ^{2}} + \frac{( y - ( - \frac{1}{33} ) ) ^{2}}{( \frac{1649}{33 2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- \frac{15}{11}, - \frac{1}{33}), a = \frac{1649}{11 6}, b = \frac{1649}{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{1649}{11 6}, b = \frac{1649}{33 2}

x^{2} + 2 y^{2} - 5 = 1

\frac{x ^{2}}{841} + \frac{y ^{2}}{484} = 1

\frac{x ^{2}}{1.586 9 ^{2}} + \frac{y ^{2}}{0.9 9 ^{2}} = 1

9 x^{2} + 18 x + 25 y^{2} + 150 y + 9 = 0

(\frac{x + 3}{2})^{2} + (y - 2)^{2} = \frac{1}{4}