x^2+y^2+y=0

Lösung

x^{2} + y^{2} + y = 0

(h, k) = (0, - \frac{1}{2}), a = \frac{1}{2}, b = \frac{1}{2}

Schritte zur Lösung

x^{2} + y^{2} + y = 0

Rewrite

x^{2} + y^{2} + y = 0

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{1}{2} ) ^{2}} + \frac{( y - ( - \frac{1}{2} ) ) ^{2}}{( \frac{1}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, - \frac{1}{2}), a = \frac{1}{2}, b = \frac{1}{2}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, - \frac{1}{2}), b = \frac{1}{2}, a = \frac{1}{2}

3 x^{2} + 5 y^{2} - 12 x + 30 y = - 42

\frac{( x - 1 ) ^{2}}{45} + \frac{( y - 2 ) ^{2}}{20} = 1

7 x^{2} + 2 y^{2} - 14 = 0

9 x^{2} + 49 y^{2} + 108 x - 196 y + 79 = 0

4 x^{2} + y^{2} = 800