1/2 x^2+1/3 y^2+1/5 x-6x+8y+2-x=0

Lösung

\frac{1}{2} x^{2} + \frac{1}{3} y^{2} + \frac{1}{5} x - 6 x + 8 y + 2 - x = 0

(h, k) = (\frac{34}{5}, - 12), a = \frac{24 6}{5}, b = \frac{72}{5}

Schritte zur Lösung

\frac{1}{2} x^{2} + \frac{1}{3} y^{2} + \frac{1}{5} x - 6 x + 8 y + 2 - x = 0

Rewrite

\frac{1}{2} x^{2} + \frac{1}{3} y^{2} + \frac{1}{5} x - 6 x + 8 y + 2 - x = 0

in the form of the standard ellipse equation

\frac{( x - \frac{34}{5} ) ^{2}}{( \frac{24 6}{5} ) ^{2}} + \frac{( y - ( - 12 ) ) ^{2}}{( \frac{72}{5} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (\frac{34}{5}, - 12), a = \frac{24 6}{5}, b = \frac{72}{5}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (\frac{34}{5}, - 12), b = \frac{72}{5}, a = \frac{24 6}{5}

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

64 y^{2} + 300 x + 100 x^{2} = - 81 + 256 y

x^{2} + y^{2} - 9 - 4 x^{2} - 9 y^{2} - 36 = 0

- 16 x^{2} - 9 y^{2} = 144

7 x^{2} + 3 y^{2} = 55