490x^{(2)}+10y^{(2)}+808x-556y+40=0

Lösung

490 x^{(2)} + 10 y^{(2)} + 808 x - 556 y + 40 = 0

(h, k) = (- \frac{202}{245}, \frac{139}{5}), a = \frac{982633}{245}, b = \frac{982633}{35}

Schritte zur Lösung

490 x^{2} + 10 y^{2} + 808 x - 556 y + 40 = 0

Rewrite

490 x^{2} + 10 y^{2} + 808 x - 556 y + 40 = 0

in the form of the standard ellipse equation

\frac{( x - ( - \frac{202}{245} ) ) ^{2}}{( \frac{982633}{245} ) ^{2}} + \frac{( y - \frac{139}{5} ) ^{2}}{( \frac{982633}{35} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- \frac{202}{245}, \frac{139}{5}), a = \frac{982633}{245}, b = \frac{982633}{35}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- \frac{202}{245}, \frac{139}{5}), b = \frac{982633}{35}, a = \frac{982633}{245}

\frac{x ^{2}}{2.3 2 ^{2}} + \frac{y ^{2}}{2.8 2 ^{2}} = 1

- 8 y^{2} + 72 = 9 x^{2}

\frac{( x + 3 ) ^{2}}{36} + \frac{( y - 4 ) ^{2}}{16} = 1

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