2x^2+y^2-2x+4y=2

Lösung

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

(h, k) = (\frac{1}{2}, - 2), a = \frac{13}{2}, b = \frac{13}{2}

Schritte zur Lösung

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - \frac{1}{2} ) ^{2}}{( \frac{13}{2} ) ^{2}} + \frac{( y - ( - 2 ) ) ^{2}}{( \frac{13}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (\frac{1}{2}, - 2), a = \frac{13}{2}, b = \frac{13}{2}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (\frac{1}{2}, - 2), b = \frac{13}{2}, a = \frac{13}{2}

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

x^{2} + 8 y^{2} = 32

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

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

\frac{x ^{2}}{8} + \frac{y ^{2}}{5} = 1