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Beliebt Geometry >

3x^2+4y^2-28x-16y+48=0

Lösung

3 x^{2} + 4 y^{2} - 28 x - 16 y + 48 = 0

Lösung

(h, k) = (\frac{14}{3}, 2), a = \frac{10}{3}, b = \frac{5}{3}

Schritte zur Lösung

3 x^{2} + 4 y^{2} - 28 x - 16 y + 48 = 0

Rewrite

3 x^{2} + 4 y^{2} - 28 x - 16 y + 48 = 0

in the form of the standard ellipse equation

\frac{( x - \frac{14}{3} ) ^{2}}{( \frac{10}{3} ) ^{2}} + \frac{( y - 2 ) ^{2}}{( \frac{5}{3} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (\frac{14}{3}, 2), a = \frac{10}{3}, b = \frac{5}{3}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (\frac{14}{3}, 2), a = \frac{10}{3}, b = \frac{5}{3}

Graph

Beliebte Beispiele

((x+3)^2)/4+((y-3)^2)/(16)=1

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

16x^2+64x+4y^2-8y+4=0

16 x^{2} + 64 x + 4 y^{2} - 8 y + 4 = 0

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

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

49 x^{2} + 4 y^{2} = 196

18y^2+24y+12x^2-12x=1

18 y^{2} + 24 y + 12 x^{2} - 12 x = 1