center 25x^2+4y^2-50x+16y-59=0

Lösung

center

25 x^{2} + 4 y^{2} - 50 x + 16 y - 59 = 0

(1, - 2)

Schritte zur Lösung

25 x^{2} + 4 y^{2} - 50 x + 16 y - 59 = 0

Rewrite

25 x^{2} + 4 y^{2} - 50 x + 16 y - 59 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (1, - 2), a = 2, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (1, - 2), b = 5, a = 2

And the center is:

(1, - 2)

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

ce n t er 25 (x + 1)^{2} + 9 (y - 2)^{2} = 225

ce n t er (\frac{( x - 2 ) ^{2}}{16}) + (\frac{y ^{2}}{9}) = 1