exzentrizität 4x^2+9y^2=13

Lösung

exzentrizität

4 x^{2} + 9 y^{2} = 13

\frac{5}{3}

Dezimale

0.74535 \dots

Schritte zur Lösung

= \frac{a ^{2} - b ^{2}}{a}

Calculate ellipse properties

4 x^{2} + 9 y^{2} = 13 :

Ellipse with center

(h, k) = (0, 0), a = \frac{13}{2}, b = \frac{13}{3}

= \frac{( \frac{13}{2} ) ^{2} - ( \frac{13}{3} ) ^{2}}{\frac{13}{2}}

\frac{( \frac{13}{2} ) ^{2} - ( \frac{13}{3} ) ^{2}}{\frac{13}{2}} = \frac{5}{3}

= \frac{5}{3}

ecce n t r i c i t y 4 - x^{2} - 4 y^{2} > 0

ecce n t r i c i t y 36 x^{2} + 16 y^{2} - 180 x + 96 y - 207 = 0

ecce n t r i c i t y \frac{( x - 4 ) ^{2}}{3} + \frac{y ^{2}}{9} = 1

ecce n t r i c i t y \frac{x ^{2}}{16} + \frac{y ^{2}}{4} = 1

ecce n t r i c i t y \frac{( x - 4 ) ^{2}}{5} + \frac{( y - 2 ) ^{2}}{4} = 1