(2x+5)^2+(3y-2)^2=(3x-4)^2+(2y+1)^2

Lösung

(2 x + 5)^{2} + (3 y - 2)^{2} = (3 x - 4)^{2} + (2 y + 1)^{2}

(h, k) = (\frac{22}{5}, \frac{8}{5}), a = \frac{4 6}{5}, b = \frac{4 6}{5}

Schritte zur Lösung

(2 x + 5)^{2} + (3 y - 2)^{2} = (3 x - 4)^{2} + (2 y + 1)^{2}

Rewrite

(2 x + 5)^{2} + (3 y - 2)^{2} - (3 x - 4)^{2} - (2 y + 1)^{2} = 0

in the form of a standard hyperbola equation

\frac{( x - \frac{22}{5} ) ^{2}}{( \frac{4 6}{5} ) ^{2}} - \frac{( y - \frac{8}{5} ) ^{2}}{( \frac{4 6}{5} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (\frac{22}{5}, \frac{8}{5}), a = \frac{4 6}{5}, b = \frac{4 6}{5}

x^{2} - 9 y^{2} - 9 = 0

y^{2} = x^{2} + 100

4 y^{2} = x^{2} + 100

\frac{y ^{2}}{64} - \frac{x ^{2}}{49} = 1

\frac{( x - 4 ) ^{2}}{9} - \frac{( y + 7 ) ^{2}}{81} = 1