2x^2+4y^2+6x-8y-5=0

Lösung

2 x^{2} + 4 y^{2} + 6 x - 8 y - 5 = 0

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

Schritte zur Lösung

2 x^{2} + 4 y^{2} + 6 x - 8 y - 5 = 0

Rewrite

2 x^{2} + 4 y^{2} + 6 x - 8 y - 5 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

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

\frac{x ^{2}}{4 ^{2}} + \frac{y ^{2}}{6 ^{2}} = 1

7 x^{2} + y^{2} = 8

4 x^{2} + 32 x + 9 y^{2} - 18 y + 37 = 0

9 (5.66 - 2) x^{2} + y^{2} = 36