25x^2+9y^2+100x+36y-89=0

Lösung

25 x^{2} + 9 y^{2} + 100 x + 36 y - 89 = 0

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

Schritte zur Lösung

25 x^{2} + 9 y^{2} + 100 x + 36 y - 89 = 0

Rewrite

25 x^{2} + 9 y^{2} + 100 x + 36 y - 89 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

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

12 x^{2} + 10 y^{2} = 120

25 x^{2} + 9 y^{2} - 50 x + 54 y - 119 = 0

16 x^{2} + 25 y^{2} + 64 x + 150 y - 111 = 0

\frac{( x - 1 ) ^{2}}{81} + \frac{( y - 2 ) ^{2}}{25} = 1