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Beliebt Geometry >

3x^2+6y^2-4x+6y-3=0

Lösung

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

Lösung

(h, k) = (\frac{2}{3}, - \frac{1}{2}), a = \frac{35}{3 2}, b = \frac{35}{6}

Schritte zur Lösung

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - \frac{2}{3} ) ^{2}}{( \frac{35}{3 2} ) ^{2}} + \frac{( y - ( - \frac{1}{2} ) ) ^{2}}{( \frac{35}{6} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (\frac{2}{3}, - \frac{1}{2}), a = \frac{35}{3 2}, b = \frac{35}{6}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (\frac{2}{3}, - \frac{1}{2}), a = \frac{35}{3 2}, b = \frac{35}{6}

Graph

Beliebte Beispiele

((x+1)^2)/4+((y-3)^2)/9 =1

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

25x^2+16y^2-100x-96y-156=0

25 x^{2} + 16 y^{2} - 100 x - 96 y - 156 = 0

(x^2)/(25)+((y-3)^2)/(16)=1

\frac{x ^{2}}{25} + \frac{( y - 3 ) ^{2}}{16} = 1

((x+2)^2}{25}+\frac{(y+1)^2)/4 =1

\frac{( x + 2 ) ^{2}}{25} + \frac{( y + 1 ) ^{2}}{4} = 1

16 - x^{2} - 4 y^{2} > 0