3x^2-9x+2y^2+10y-6=0

Lösung

3 x^{2} - 9 x + 2 y^{2} + 10 y - 6 = 0

(h, k) = (\frac{3}{2}, - \frac{5}{2}), a = \frac{101}{2 3}, b = \frac{101}{2 2}

Schritte zur Lösung

3 x^{2} - 9 x + 2 y^{2} + 10 y - 6 = 0

Rewrite

3 x^{2} - 9 x + 2 y^{2} + 10 y - 6 = 0

in the form of the standard ellipse equation

\frac{( x - \frac{3}{2} ) ^{2}}{( \frac{101}{2 3} ) ^{2}} + \frac{( y - ( - \frac{5}{2} ) ) ^{2}}{( \frac{101}{2 2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (\frac{3}{2}, - \frac{5}{2}), a = \frac{101}{2 3}, b = \frac{101}{2 2}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (\frac{3}{2}, - \frac{5}{2}), b = \frac{101}{2 2}, a = \frac{101}{2 3}

x^{2} + y^{2} = 10 - x^{2} - 2 y^{2}

- \frac{x ^{2}}{9} - y^{2} = 1

128 + 16 y - x^{2} - 4 y^{2} \geq 0

144 y^{2} + 169 x^{2} = 169

9 (x + y i)^{2} + 9 (x - y i)^{2} + 82 (x + y i) (x - y i) = 1600