16x^2+25y^2-96x+100y-156=0

Lösung

16 x^{2} + 25 y^{2} - 96 x + 100 y - 156 = 0

(h, k) = (3, - 2), a = 5, b = 4

Schritte zur Lösung

16 x^{2} + 25 y^{2} - 96 x + 100 y - 156 = 0

Rewrite

16 x^{2} + 25 y^{2} - 96 x + 100 y - 156 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (3, - 2), a = 5, b = 4

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (3, - 2), a = 5, b = 4

x^{2} + 4 y^{2} - 6 x + 8 y - 3 = 0

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

25 x^{2} + 36 y^{2} + 100 x + 72 y - 764 = 0

12 x^{2} + 4 y^{2} - 24 x - 4 y + 1 = 0

36 x^{2} + 16 y^{2} - 180 x + 96 y - 207 = 0