(x^2+y^2-x)/(2x-x^2-y^2)>= 0

Lösung

\frac{x ^{2} + y ^{2} - x}{2 x - x ^{2} - y ^{2}} \geq 0

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

Schritte zur Lösung

\frac{x ^{2} + y ^{2} - x}{2 x - x ^{2} - y ^{2}} \geq 0

Rewrite

\frac{x ^{2} + y ^{2} - x}{2 x - x ^{2} - y ^{2}} \geq 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

4 x^{2} + y^{2} - 16 x + 6 y - 75 = 0

4 x^{2} - 24 x + \frac{y ^{2}}{16} + \frac{y}{8} + \frac{573}{16} = 0

\frac{( x - 2 ) ^{2}}{64} + \frac{( y + 4 ) ^{2}}{16} = 1

25 x^{2} + 16 y^{2} - 250 x - 32 y + 241 = 0

9 x^{2} + 5 y^{2} = 45