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Beliebt Geometry >

3x^2+2y^2-12x+6y-10=0

Lösung

3 x^{2} + 2 y^{2} - 12 x + 6 y - 10 = 0

Lösung

(h, k) = (2, - \frac{3}{2}), a = \frac{53}{6}, b = \frac{53}{2}

Schritte zur Lösung

3 x^{2} + 2 y^{2} - 12 x + 6 y - 10 = 0

Rewrite

3 x^{2} + 2 y^{2} - 12 x + 6 y - 10 = 0

in the form of the standard ellipse equation

\frac{( x - 2 ) ^{2}}{( \frac{53}{6} ) ^{2}} + \frac{( y - ( - \frac{3}{2} ) ) ^{2}}{( \frac{53}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (2, - \frac{3}{2}), a = \frac{53}{6}, b = \frac{53}{2}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (2, - \frac{3}{2}), b = \frac{53}{2}, a = \frac{53}{6}

Graph

Beliebte Beispiele

4.14x^2+3.92y^2-41.82x-82.62y+78=0

4.14 x^{2} + 3.92 y^{2} - 41.82 x - 82.62 y + 78 = 0

36 x^{2} + 8 y^{2} = 98

(x^2}{64}+\frac{y^2)/9 =1

\frac{x ^{2}}{64} + \frac{y ^{2}}{9} = 1

2x^2+5y^2+3x+30y-16=0

2 x^{2} + 5 y^{2} + 3 x + 30 y - 16 = 0

8 x^{2} + y^{2} = 10