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Beliebt Geometry >

4a2-9b2=(2a2+3b2)(2a2-3b2)

Lösung

4 a 2 - 9 b 2 = (2 a 2 + 3 b 2) (2 a 2 - 3 b 2)

Lösung

(h, k) = (\frac{1}{4}, \frac{1}{4}), a = \frac{5}{12}, b = \frac{5}{8}

Schritte zur Lösung

4 a \cdot 2 - 9 b \cdot 2 = (2 a \cdot 2 + 3 b \cdot 2) (2 a \cdot 2 - 3 b \cdot 2)

Rewrite

4 a 2 - 9 b 2 - (2 a 2 + 3 b 2) (2 a 2 - 3 b 2) = 0

in the form of a standard hyperbola equation

\frac{( b - \frac{1}{4} ) ^{2}}{( \frac{5}{12} ) ^{2}} - \frac{( a - \frac{1}{4} ) ^{2}}{( \frac{5}{8} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (\frac{1}{4}, \frac{1}{4}), a = \frac{5}{12}, b = \frac{5}{8}

Graph

Beliebte Beispiele

25x^2-9y^2+50x-36y-236=0

25 x^{2} - 9 y^{2} + 50 x - 36 y - 236 = 0

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

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

x^{2} - y^{2} - 6 x - 7 = 0

x^{(2)}-6=((y^{(2)}))/((3))

x^{(2)} - 6 = \frac{( y ^{(2)} )}{( 3 )}

(x^2)/9+(2x)/3-9y^2-54y-81=0

\frac{x ^{2}}{9} + \frac{2 x}{3} - 9 y^{2} - 54 y - 81 = 0