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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

(x^2)/(81/4)+(y^2)/(25/16)=1

\frac{x ^{2}}{\frac{81}{4}} + \frac{y ^{2}}{\frac{25}{16}} = 1

9x^2+16y^2+72x+128y+256=0

9 x^{2} + 16 y^{2} + 72 x + 128 y + 256 = 0

9x^2+4y^2-18x-16y-11=0

9 x^{2} + 4 y^{2} - 18 x - 16 y - 11 = 0

x^{2} + 4 y^{2} - 25 = 0

4x^2+y^2+2y-35=0

4 x^{2} + y^{2} + 2 y - 35 = 0