4x^2-16y^2-10x+21y-27=0

Lösung

4 x^{2} - 16 y^{2} - 10 x + 21 y - 27 = 0

(h, k) = (\frac{5}{4}, \frac{21}{32}), a = \frac{1687}{16}, b = \frac{1687}{32}

Schritte zur Lösung

4 x^{2} - 16 y^{2} - 10 x + 21 y - 27 = 0

Rewrite

4 x^{2} - 16 y^{2} - 10 x + 21 y - 27 = 0

in the form of a standard hyperbola equation

\frac{( x - \frac{5}{4} ) ^{2}}{( \frac{1687}{16} ) ^{2}} - \frac{( y - \frac{21}{32} ) ^{2}}{( \frac{1687}{32} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (\frac{5}{4}, \frac{21}{32}), a = \frac{1687}{16}, b = \frac{1687}{32}

\frac{x ^{2}}{3} - \frac{y ^{2}}{4} = 1

y^{2} - x^{2} = \frac{4}{25}

\frac{x ^{2}}{58} - \frac{y ^{2}}{120} = 1

\frac{( x - 5 ) ^{2}}{36} - \frac{( y - 2 ) ^{2}}{16} = 1

y^{2} - 9 x^{2} - 4 y + 18 x = 86