center 4x^2+5y^2-2x+78y-83=x-3y+3

Lösung

center

4 x^{2} + 5 y^{2} - 2 x + 78 y - 83 = x - 3 y + 3

(\frac{3}{8}, - \frac{81}{10})

Schritte zur Lösung

4 x^{2} + 5 y^{2} - 2 x + 78 y - 83 = x - 3 y + 3

Rewrite

4 x^{2} + 5 y^{2} - 2 x + 78 y - 83 - x + 3 y - 3 = 0

in the form of the standard ellipse equation

\frac{( x - \frac{3}{8} ) ^{2}}{( \frac{33169}{8 5} ) ^{2}} + \frac{( y - ( - \frac{81}{10} ) ) ^{2}}{( \frac{33169}{20} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (\frac{3}{8}, - \frac{81}{10}), a = \frac{33169}{8 5}, b = \frac{33169}{20}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (\frac{3}{8}, - \frac{81}{10}), a = \frac{33169}{8 5}, b = \frac{33169}{20}

And the center is:

(\frac{3}{8}, - \frac{81}{10})

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