1/3 3x^2+3y^2-8x-8y*31=0

Lösung

\frac{1}{3} 3 x^{2} + 3 y^{2} - 8 x - 8 y \cdot 31 = 0

(h, k) = (4, \frac{124}{3}), a = \frac{8 241}{3}, b = \frac{8 241}{3}

Schritte zur Lösung

\frac{1}{3} \cdot 3 x^{2} + 3 y^{2} - 8 x - 8 y \cdot 31 = 0

Rewrite

\frac{1}{3} 3 x^{2} + 3 y^{2} - 8 x - 8 y \cdot 31 = 0

in the form of the standard ellipse equation

\frac{( x - 4 ) ^{2}}{( \frac{8 241}{3} ) ^{2}} + \frac{( y - \frac{124}{3} ) ^{2}}{( \frac{8 241}{3} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (4, \frac{124}{3}), a = \frac{8 241}{3}, b = \frac{8 241}{3}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (4, \frac{124}{3}), a = \frac{8 241}{3}, b = \frac{8 241}{3}

2 x^{2} + 3 y^{2} - 18 = 0

49 x^{2} + 16 y^{2} - 588 x + 128 y + 1236 = 0

18 x^{2} + 24 y + 12 y^{2} - 12 x = 1

2 x^{2} + y^{2} \leq 8

x^{2} + 4 y^{2} - 12 x - 16 y = 48