center 9x^2+4y^2+54x-8y+49=0

Lösung

center

9 x^{2} + 4 y^{2} + 54 x - 8 y + 49 = 0

(- 3, 1)

Schritte zur Lösung

9 x^{2} + 4 y^{2} + 54 x - 8 y + 49 = 0

Rewrite

9 x^{2} + 4 y^{2} + 54 x - 8 y + 49 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 3, 1), a = 2, b = 3

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 3, 1), b = 3, a = 2

And the center is:

(- 3, 1)

ce n t er \frac{( x - 3 ) ^{2}}{25} + \frac{( y + 2 ) ^{2}}{36} = 1

ce n t er 16 x^{2} + 25 y^{2} - 128 x + 150 y + 81 = 0

ce n t er 11 x^{2} + 3 x + 3 y^{2} + 11 y = 0

ce n t er 9 x^{2} + 16 y^{2} - 18 x + 96 y - 279 = 0

ce n t er 20 x^{2} - 16 y^{2} - 40 x 128 x - 556 = 0