25x^2+9y^2-100y+18x-116=0

Lösung

25 x^{2} + 9 y^{2} - 100 y + 18 x - 116 = 0

(h, k) = (- \frac{9}{25}, \frac{50}{9}), a = \frac{89329}{75}, b = \frac{89329}{45}

Schritte zur Lösung

25 x^{2} + 9 y^{2} - 100 y + 18 x - 116 = 0

Rewrite

25 x^{2} + 9 y^{2} - 100 y + 18 x - 116 = 0

in the form of the standard ellipse equation

\frac{( x - ( - \frac{9}{25} ) ) ^{2}}{( \frac{89329}{75} ) ^{2}} + \frac{( y - \frac{50}{9} ) ^{2}}{( \frac{89329}{45} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- \frac{9}{25}, \frac{50}{9}), a = \frac{89329}{75}, b = \frac{89329}{45}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- \frac{9}{25}, \frac{50}{9}), b = \frac{89329}{45}, a = \frac{89329}{75}

2 x^{2} + 3 y^{2} + 4 x - 5 y - 6 = 0

2 y - x^{2} - y^{2} > 0

25 x^{2} + 36 y^{2} = 900

(\frac{2 x ^{2}}{25}) + (\frac{( y - 3 ) ^{2}}{49}) = 1

(x + 2)^{2} - 1 = - 4 (y + 1)^{2}