16x^{(2)}+25y^{(2)}-128x+100y=0

Lösung

16 x^{(2)} + 25 y^{(2)} - 128 x + 100 y = 0

(h, k) = (4, - 2), a = \frac{89}{2}, b = \frac{2 89}{5}

Schritte zur Lösung

16 x^{2} + 25 y^{2} - 128 x + 100 y = 0

Rewrite

16 x^{2} + 25 y^{2} - 128 x + 100 y = 0

in the form of the standard ellipse equation

\frac{( x - 4 ) ^{2}}{( \frac{89}{2} ) ^{2}} + \frac{( y - ( - 2 ) ) ^{2}}{( \frac{2 89}{5} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (4, - 2), a = \frac{89}{2}, b = \frac{2 89}{5}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (4, - 2), a = \frac{89}{2}, b = \frac{2 89}{5}

\frac{( x + 2 ) ^{2}}{64} + \frac{( y - 8 ) ^{2}}{36} = 1

16 x^{2} + 25 y^{2} = \frac{169}{4}

9 x^{2} + 5 y^{2} = 180

\frac{( x - 2 ) ^{2}}{36} + \frac{( y + 5 ) ^{2}}{29} = 1

\frac{( x - 4 ) ^{2}}{36} + \frac{( y + 1 ) ^{2}}{10} = 1