3x^2+y^2+20x+32=0

Lösung

3 x^{2} + y^{2} + 20 x + 32 = 0

(h, k) = (- \frac{10}{3}, 0), a = \frac{2}{3}, b = \frac{2}{3}

Schritte zur Lösung

3 x^{2} + y^{2} + 20 x + 32 = 0

Rewrite

3 x^{2} + y^{2} + 20 x + 32 = 0

in the form of the standard ellipse equation

\frac{( x - ( - \frac{10}{3} ) ) ^{2}}{( \frac{2}{3} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{2}{3} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- \frac{10}{3}, 0), a = \frac{2}{3}, b = \frac{2}{3}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- \frac{10}{3}, 0), b = \frac{2}{3}, a = \frac{2}{3}

y^{2} = 1 - 2 x^{2}

x^{2} + 2 z^{2} + 6 x - 8 z + 1 = 0

4 x^{2} + y^{2} + 8 x = 0

28 x^{2} + 64 y^{2} - 28 x + 128 y - 377 = 0

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