25x^2+9y^2-100x+18y-118=0

Lösung

25 x^{2} + 9 y^{2} - 100 x + 18 y - 118 = 0

(h, k) = (2, - 1), a = \frac{227}{5}, b = \frac{227}{3}

Schritte zur Lösung

25 x^{2} + 9 y^{2} - 100 x + 18 y - 118 = 0

Rewrite

25 x^{2} + 9 y^{2} - 100 x + 18 y - 118 = 0

in the form of the standard ellipse equation

\frac{( x - 2 ) ^{2}}{( \frac{227}{5} ) ^{2}} + \frac{( y - ( - 1 ) ) ^{2}}{( \frac{227}{3} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (2, - 1), a = \frac{227}{5}, b = \frac{227}{3}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (2, - 1), b = \frac{227}{3}, a = \frac{227}{5}

2 x^{2} + 6 y^{2} = 12

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

- x^{2} - 9 y^{2} - 63 = 0

x^{(2)} + 4 y^{(2)} + 7 = 12 y - 2 x

\frac{( x - 4 ) ^{2}}{4} + \frac{( y - 5 ) ^{2}}{36} = 1