6x+3y*2=4+2x^2+5y^2

Lösung

6 x + 3 y \cdot 2 = 4 + 2 x^{2} + 5 y^{2}

(h, k) = (\frac{3}{2}, \frac{3}{5}), a = \frac{23}{2 5}, b = \frac{23}{5 2}

Schritte zur Lösung

6 x + 3 y \cdot 2 = 4 + 2 x^{2} + 5 y^{2}

Rewrite

6 x + 3 y \cdot 2 = 4 + 2 x^{2} + 5 y^{2}

in the form of the standard ellipse equation

\frac{( x - \frac{3}{2} ) ^{2}}{( \frac{23}{2 5} ) ^{2}} + \frac{( y - \frac{3}{5} ) ^{2}}{( \frac{23}{5 2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (\frac{3}{2}, \frac{3}{5}), a = \frac{23}{2 5}, b = \frac{23}{5 2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (\frac{3}{2}, \frac{3}{5}), a = \frac{23}{2 5}, b = \frac{23}{5 2}

\frac{( x + 2 ) ^{2}}{9} + \frac{( y - 4 ) ^{2}}{16} = 1

25 x^{2} + 64 y^{2} = 1600

\frac{x ^{2}}{25} + \frac{y ^{2}}{76} = 1

2 y^{2} = 4 - 5 x^{2}

\frac{( x - 4 ) ^{2}}{9} + \frac{( y - 3 ) ^{2}}{16} = 1