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Beliebt Geometry >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Rewrite

4 x^{2} - 16 x + 9 y^{2} + 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+16y^2-18x+64y=71

9 x^{2} + 16 y^{2} - 18 x + 64 y = 71

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

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

(x^2)/9+(y^2)/4 =y+6

\frac{x ^{2}}{9} + \frac{y ^{2}}{4} = y + 6

4x^2-2x+9y^2+6y=41

4 x^{2} - 2 x + 9 y^{2} + 6 y = 41

((x-3)^2}{16}+(\frac{y+2)/9)^2=1

\frac{( x - 3 ) ^{2}}{16} + (\frac{y + 2}{9})^{2} = 1