center 9x^2+25y^2+108x-200y+499=0

Lösung

center

9 x^{2} + 25 y^{2} + 108 x - 200 y + 499 = 0

(- 6, 4)

Schritte zur Lösung

9 x^{2} + 25 y^{2} + 108 x - 200 y + 499 = 0

Rewrite

9 x^{2} + 25 y^{2} + 108 x - 200 y + 499 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 6 ) ) ^{2}}{5 ^{2}} + \frac{( y - 4 ) ^{2}}{3 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 6, 4), a = 5, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 6, 4), a = 5, b = 3

And the center is:

(- 6, 4)

ce n t er 4 x^{2} + 9 y^{2} = 25

ce n t er 3 x^{(2)} + 2 y^{(2)} - 12 x + 8 y + 19 = 0

ce n t er 3 x^{2} + y^{2} + 2 x - 6 y = 3

ce n t er x^{2} + \frac{( y + 2 ) ^{2}}{4} = 1

ce n t er x^{2} + 9 y^{2} - 14 x + 36 y + 49 = 0