5x^2-4y^2-18y+9=0

Lösung

5 x^{2} - 4 y^{2} - 18 y + 9 = 0

(h, k) = (0, - \frac{9}{4}), a = \frac{3 13}{4}, b = \frac{3 13}{2 5}

Schritte zur Lösung

5 x^{2} - 4 y^{2} - 18 y + 9 = 0

Rewrite

5 x^{2} - 4 y^{2} - 18 y + 9 = 0

in the form of a standard hyperbola equation

\frac{( y - ( - \frac{9}{4} ) ) ^{2}}{( \frac{3 13}{4} ) ^{2}} - \frac{( x - 0 ) ^{2}}{( \frac{3 13}{2 5} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, - \frac{9}{4}), a = \frac{3 13}{4}, b = \frac{3 13}{2 5}

\frac{( x + 3 ) ^{2}}{4} - \frac{( y + 1 ) ^{2}}{9} = 1

\frac{( y + 3 ) ^{2}}{81} - \frac{( x + 3 ) ^{2}}{16} = 1

(x - 4)^{2} - (y - 4)^{2} \leq 9

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

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