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Beliebt Geometry >

4x^2+9y^2-16x-54y+61=0

Lösung

4 x^{2} + 9 y^{2} - 16 x - 54 y + 61 = 0

Lösung

(h, k) = (2, 3), a = 3, b = 2

Schritte zur Lösung

4 x^{2} + 9 y^{2} - 16 x - 54 y + 61 = 0

Rewrite

4 x^{2} + 9 y^{2} - 16 x - 54 y + 61 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (2, 3), a = 3, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (2, 3), a = 3, b = 2

Graph

Beliebte Beispiele

9x^2+25y^2-100y-125=0

9 x^{2} + 25 y^{2} - 100 y - 125 = 0

x^2+4y^2+10x+10y-8=0

x^{2} + 4 y^{2} + 10 x + 10 y - 8 = 0

(x^2)/(25)+(z^2)/(64)=1

\frac{x ^{2}}{25} + \frac{z ^{2}}{64} = 1

x^2+4y^2+20x-40y=-100

x^{2} + 4 y^{2} + 20 x - 40 y = - 100

a^{2} + 2 b^{2} = 10