2x^2+4y^2+9x+9y-17=0

Lösung

2 x^{2} + 4 y^{2} + 9 x + 9 y - 17 = 0

(h, k) = (- \frac{9}{4}, - \frac{9}{8}), a = \frac{515}{4 2}, b = \frac{515}{8}

Schritte zur Lösung

2 x^{2} + 4 y^{2} + 9 x + 9 y - 17 = 0

Rewrite

2 x^{2} + 4 y^{2} + 9 x + 9 y - 17 = 0

in the form of the standard ellipse equation

\frac{( x - ( - \frac{9}{4} ) ) ^{2}}{( \frac{515}{4 2} ) ^{2}} + \frac{( y - ( - \frac{9}{8} ) ) ^{2}}{( \frac{515}{8} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- \frac{9}{4}, - \frac{9}{8}), a = \frac{515}{4 2}, b = \frac{515}{8}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- \frac{9}{4}, - \frac{9}{8}), a = \frac{515}{4 2}, b = \frac{515}{8}

x^{2} + 4 y^{2} - 2 x + 4 y + 1 = 0

16 x^{2} + 4 y^{2} + 96 x - 8 y + 84 = 0

\frac{x ^{2}}{23} + \frac{y ^{2}}{19} = 1

4 x^{2} + 24 x + 36 + 36 y^{2} - 360 y + 756 = 0

9 x^{2} + 36 y^{2} - 54 x + 72 y - 207 = 0