x^2+y^2-21/8 x+19/4-525/8 =0

Lösung

x^{2} + y^{2} - \frac{21}{8} x + \frac{19}{4} - \frac{525}{8} = 0

(h, k) = (\frac{21}{16}, 0), a = \frac{5 641}{16}, b = \frac{5 641}{16}

Schritte zur Lösung

x^{2} + y^{2} - \frac{21}{8} x + \frac{19}{4} - \frac{525}{8} = 0

Rewrite

x^{2} + y^{2} - \frac{21}{8} x + \frac{19}{4} - \frac{525}{8} = 0

in the form of the standard ellipse equation

\frac{( x - \frac{21}{16} ) ^{2}}{( \frac{5 641}{16} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{5 641}{16} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (\frac{21}{16}, 0), a = \frac{5 641}{16}, b = \frac{5 641}{16}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (\frac{21}{16}, 0), b = \frac{5 641}{16}, a = \frac{5 641}{16}

25 x^{2} + 16 y^{2} + 200 x + 64 y + 64 = 0

9 x^{(2)} + 16 y^{(2)} - 54 x + 64 y + 1 = 0

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

- 2 x^{2} + 1 - y^{2} = 0

2 x^{2} + 3 y^{2} + 4 x - 6 y - 1 = 0