center 6x^2+9y^2-18y-45=0

Lösung

center

6 x^{2} + 9 y^{2} - 18 y - 45 = 0

(0, 1)

Schritte zur Lösung

6 x^{2} + 9 y^{2} - 18 y - 45 = 0

Rewrite

6 x^{2} + 9 y^{2} - 18 y - 45 = 0

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{3 ^{2}} + \frac{( y - 1 ) ^{2}}{( 6 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 1), a = 3, b = 6

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 1), a = 3, b = 6

And the center is:

(0, 1)

ce n t er \frac{( x - 3 ) ^{2}}{25} + \frac{( y + 2 ) ^{2}}{81} = 1

ce n t er 25 x^{2} + 4 y^{2} - 50 x + 16 y - 59 = 0

ce n t er 9 x^{2} + 16 y^{2} = 576

ce n t er \frac{( x - 10 ) ^{2}}{4} + \frac{y ^{2}}{16} = 1

ce n t er 25 x^{2} + 16 y^{2} + 100 x - 96 y = 156