2/4 (3x^2+y^2)-sqrt(2)(x-y)=0

Lösung

\frac{2}{4} (3 x^{2} + y^{2}) - 2 (x - y) = 0

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

Schritte zur Lösung

\frac{2}{4} (3 x^{2} + y^{2}) - 2 (x - y) = 0

Rewrite

\frac{2}{4} (3 x^{2} + y^{2}) - 2 (x - y) = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

8 (x + \frac{6}{7})^{2} + 3 (y - \frac{3}{2})^{2} = 27

\frac{( y - 2 ) ^{2}}{4} + \frac{( z - 3 ) ^{2}}{1} = 1

\frac{( x + 1 ) ^{2}}{16} + \frac{( y + 1 ) ^{2}}{9} = 1

a^{2} + 2 b^{2} = 1

- 25 x^{2} - 4 y^{2} + 100 = 4