-3y^2-3x^2+5x+10y=5x^2+1

Lösung

- 3 y^{2} - 3 x^{2} + 5 x + 10 y = 5 x^{2} + 1

(h, k) = (\frac{5}{16}, \frac{5}{3}), a = \frac{779}{16 3}, b = \frac{779}{12 2}

Schritte zur Lösung

- 3 y^{2} - 3 x^{2} + 5 x + 10 y = 5 x^{2} + 1

Rewrite

- 3 y^{2} - 3 x^{2} + 5 x + 10 y - 5 x^{2} - 1 = 0

in the form of the standard ellipse equation

\frac{( x - \frac{5}{16} ) ^{2}}{( \frac{779}{16 3} ) ^{2}} + \frac{( y - \frac{5}{3} ) ^{2}}{( \frac{779}{12 2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (\frac{5}{16}, \frac{5}{3}), a = \frac{779}{16 3}, b = \frac{779}{12 2}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (\frac{5}{16}, \frac{5}{3}), b = \frac{779}{12 2}, a = \frac{779}{16 3}

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

10 x^{2} + 40 x + 7 y^{2} + 70 y + 145 = 0

6 = x^{2} + 9 y^{2}

(3 x - 3)^{2} + (- 2 y - 4)^{2} = 43 + 9 + 16

36 x^{2} + 81 y^{2} = 49