3x^2+2x-3y^2+14y=-24

Lösung

3 x^{2} + 2 x - 3 y^{2} + 14 y = - 24

(h, k) = (- \frac{1}{3}, \frac{7}{3}), a = \frac{2 10}{3}, b = \frac{2 10}{3}

Schritte zur Lösung

3 x^{2} + 2 x - 3 y^{2} + 14 y = - 24

Rewrite

3 x^{2} + 2 x - 3 y^{2} + 14 y = - 24

in the form of a standard hyperbola equation

\frac{( y - \frac{7}{3} ) ^{2}}{( \frac{2 10}{3} ) ^{2}} - \frac{( x - ( - \frac{1}{3} ) ) ^{2}}{( \frac{2 10}{3} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- \frac{1}{3}, \frac{7}{3}), a = \frac{2 10}{3}, b = \frac{2 10}{3}

so l v e f or x, K (x)^{2} = 4 (128 x + x^{2})

\frac{( x - 1 ) ^{2}}{9} - \frac{( y - 5 ) ^{2}}{16} = 1

9 x^{2} - 16 y^{2} - 18 x - 64 y - 200 = 0

4 x^{2} - 16 y^{2} - 64 y - 128 = 0

x^{2} + 5^{2} = y^{2}