25x^2+4y^2-8x+200y+304=0

Lösung

25 x^{2} + 4 y^{2} - 8 x + 200 y + 304 = 0

(h, k) = (\frac{4}{25}, - 25), a = \frac{2 13729}{25}, b = \frac{13729}{5}

Schritte zur Lösung

25 x^{2} + 4 y^{2} - 8 x + 200 y + 304 = 0

Rewrite

25 x^{2} + 4 y^{2} - 8 x + 200 y + 304 = 0

in the form of the standard ellipse equation

\frac{( x - \frac{4}{25} ) ^{2}}{( \frac{2 13729}{25} ) ^{2}} + \frac{( y - ( - 25 ) ) ^{2}}{( \frac{13729}{5} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (\frac{4}{25}, - 25), a = \frac{2 13729}{25}, b = \frac{13729}{5}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (\frac{4}{25}, - 25), b = \frac{13729}{5}, a = \frac{2 13729}{25}

2 x^{2} + y^{2} + 2 y = 1

\frac{x ^{2}}{25} + \frac{( y - 2 ) ^{2}}{4} = 1

\frac{( x + 7 ) ^{2}}{16} + \frac{( y + 5 ) ^{2}}{4} = 1

y^{2} = 9 - 4 x^{2}

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