13x^2+23y^2-51x-19y-4=0

Lösung

13 x^{2} + 23 y^{2} - 51 x - 19 y - 4 = 0

(h, k) = (\frac{51}{26}, \frac{19}{46}), a = \frac{15 77}{13 23}, b = \frac{15 77}{23 13}

Schritte zur Lösung

13 x^{2} + 23 y^{2} - 51 x - 19 y - 4 = 0

Rewrite

13 x^{2} + 23 y^{2} - 51 x - 19 y - 4 = 0

in the form of the standard ellipse equation

\frac{( x - \frac{51}{26} ) ^{2}}{( \frac{15 77}{13 23} ) ^{2}} + \frac{( y - \frac{19}{46} ) ^{2}}{( \frac{15 77}{23 13} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (\frac{51}{26}, \frac{19}{46}), a = \frac{15 77}{13 23}, b = \frac{15 77}{23 13}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (\frac{51}{26}, \frac{19}{46}), a = \frac{15 77}{13 23}, b = \frac{15 77}{23 13}

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