1x^2+3y^2+9x+8y-14=0

Lösung

1 x^{2} + 3 y^{2} + 9 x + 8 y - 14 = 0

(h, k) = (- \frac{9}{2}, - \frac{4}{3}), a = \frac{5 19}{2 3}, b = \frac{5 19}{6}

Schritte zur Lösung

1 \cdot x^{2} + 3 y^{2} + 9 x + 8 y - 14 = 0

Rewrite

1 x^{2} + 3 y^{2} + 9 x + 8 y - 14 = 0

in the form of the standard ellipse equation

\frac{( x - ( - \frac{9}{2} ) ) ^{2}}{( \frac{5 19}{2 3} ) ^{2}} + \frac{( y - ( - \frac{4}{3} ) ) ^{2}}{( \frac{5 19}{6} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- \frac{9}{2}, - \frac{4}{3}), a = \frac{5 19}{2 3}, b = \frac{5 19}{6}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- \frac{9}{2}, - \frac{4}{3}), a = \frac{5 19}{2 3}, b = \frac{5 19}{6}

25 x^{2} + 16 y^{2} + 100 x - 64 y - 236 = 0

3 x^{2} + 4 y^{2} + 18 x - 16 y + 31 = 0

\frac{( x - 2 ) ^{2}}{9} + \frac{( y + 1 ) ^{2}}{36} = 1

\frac{x ^{2}}{5} + \frac{y ^{2}}{8} = 1

4 X^{2} + 9 Y^{2} - 32 X - 36 Y + 64 = 0