x^2+8y^2+54x-48y+8=0

Lösung

x^{2} + 8 y^{2} + 54 x - 48 y + 8 = 0

(h, k) = (- 27, 3), a = 793, b = \frac{793}{2 2}

Schritte zur Lösung

x^{2} + 8 y^{2} + 54 x - 48 y + 8 = 0

Rewrite

x^{2} + 8 y^{2} + 54 x - 48 y + 8 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 27 ) ) ^{2}}{( 793 ) ^{2}} + \frac{( y - 3 ) ^{2}}{( \frac{793}{2 2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 27, 3), a = 793, b = \frac{793}{2 2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 27, 3), a = 793, b = \frac{793}{2 2}

4 x^{2} + 4 y^{2} + 16 y = 0

9 (x - 6)^{2} + 64 (y - 4)^{2} = 576

6 x + 3 y \cdot 2 = 4 + 2 x^{2} + 5 y^{2}

\frac{( x + 2 ) ^{2}}{9} + \frac{( y - 4 ) ^{2}}{16} = 1

25 x^{2} + 64 y^{2} = 1600