achse 3x^2+4y^2+27x-16y+48=0

Lösung

achse

3 x^{2} + 4 y^{2} + 27 x - 16 y + 48 = 0

semi - major axis a = \frac{115}{2 3}, semi - minor axis b = \frac{115}{4}

Schritte zur Lösung

3 x^{2} + 4 y^{2} + 27 x - 16 y + 48 = 0

Rewrite

3 x^{2} + 4 y^{2} + 27 x - 16 y + 48 = 0

in the form of the standard ellipse equation

\frac{( x - ( - \frac{9}{2} ) ) ^{2}}{( \frac{115}{2 3} ) ^{2}} + \frac{( y - 2 ) ^{2}}{( \frac{115}{4} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- \frac{9}{2}, 2), a = \frac{115}{2 3}, b = \frac{115}{4}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- \frac{9}{2}, 2), a = \frac{115}{2 3}, b = \frac{115}{4}

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a x i s \frac{( x - 4 ) ^{2}}{64} + \frac{( y - 2 ) ^{2}}{39} = 1

a x i s \frac{( x - 1 ) ^{2}}{13} + \frac{( y + 5 ) ^{2}}{12} = 1