center 4x^2+9y^2-24x+72y+144=0

Lösung

center

4 x^{2} + 9 y^{2} - 24 x + 72 y + 144 = 0

(3, - 4)

Schritte zur Lösung

4 x^{2} + 9 y^{2} - 24 x + 72 y + 144 = 0

Rewrite

4 x^{2} + 9 y^{2} - 24 x + 72 y + 144 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (3, - 4), a = 3, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (3, - 4), a = 3, b = 2

And the center is:

(3, - 4)

ce n t er \frac{x ^{2}}{64} + \frac{y ^{2}}{36} = 1

ce n t er \frac{x ^{2}}{64} + \frac{y ^{2}}{100} = 1

ce n t er 9 x^{2} + 16 y^{2} - 54 x + 64 y + 1 = 0

ce n t er 9 x^{2} + 16 y^{2} - 72 x + 64 y - 368 = 0

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