center 9x^2+18x+4y^2-24y+9=0

Lösung

center

9 x^{2} + 18 x + 4 y^{2} - 24 y + 9 = 0

(- 1, 3)

Schritte zur Lösung

9 x^{2} + 18 x + 4 y^{2} - 24 y + 9 = 0

Rewrite

9 x^{2} + 18 x + 4 y^{2} - 24 y + 9 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

And the center is:

(- 1, 3)

ce n t er 4 x^{2} + 9 y^{2} = 144

ce n t er x^{2} - 8 x + 8 y^{2} + 12 y = 0

ce n t er x^{2} + 4 y^{2} - 6 x + 20 y - 2 = 0

ce n t er x^{2} + y^{2} + 10 y = 0

ce n t er 36 x^{2} + 9 y^{2} + 36 y - 288 = 0