x^2+4y^2-6x+12y-11=0

Lösung

x^{2} + 4 y^{2} - 6 x + 12 y - 11 = 0

(h, k) = (3, - \frac{3}{2}), a = 29, b = \frac{29}{2}

Schritte zur Lösung

x^{2} + 4 y^{2} - 6 x + 12 y - 11 = 0

Rewrite

x^{2} + 4 y^{2} - 6 x + 12 y - 11 = 0

in the form of the standard ellipse equation

\frac{( x - 3 ) ^{2}}{( 29 ) ^{2}} + \frac{( y - ( - \frac{3}{2} ) ) ^{2}}{( \frac{29}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (3, - \frac{3}{2}), a = 29, b = \frac{29}{2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (3, - \frac{3}{2}), a = 29, b = \frac{29}{2}

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

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

x (100 - 3 x) + y (192 - 6 y) = 0

3 x^{2} + 4 y^{2} + 24 x - 16 y + 52 = 0

\frac{( x - 6 ) ^{2}}{36} + \frac{( y + 4 ) ^{2}}{16} = 1