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solvefor a,(x^2+y^2)^2=a^2(x^2-y^2)

解答

求解

a, (x^{2} + y^{2})^{2} = a^{2} (x^{2} - y^{2})

解答

a = \frac{x ^{2} + y ^{2}}{x ^{2} - y ^{2}}, a = - \frac{x ^{2} + y ^{2}}{x ^{2} - y ^{2}}; x^{2} - y^{2} \neq = 0

求解步骤

(x^{2} + y^{2})^{2} = a^{2} (x^{2} - y^{2})

交换两边

a^{2} (x^{2} - y^{2}) = (x^{2} + y^{2})^{2}

两边除以

x^{2} - y^{2}; x^{2} - y^{2} \neq = 0

a^{2} = \frac{( x ^{2} + y ^{2} ) ^{2}}{x ^{2} - y ^{2}}; x^{2} - y^{2} \neq = 0

对于

x^{2} = f (a)

解为

x = f (a), - f (a)

a = \frac{( x ^{2} + y ^{2} ) ^{2}}{x ^{2} - y ^{2}}, a = - \frac{( x ^{2} + y ^{2} ) ^{2}}{x ^{2} - y ^{2}}; x^{2} - y^{2} \neq = 0

化简

\frac{( x ^{2} + y ^{2} ) ^{2}}{x ^{2} - y ^{2}} : \frac{x ^{2} + y ^{2}}{x ^{2} - y ^{2}}

化简

- \frac{( x ^{2} + y ^{2} ) ^{2}}{x ^{2} - y ^{2}} : - \frac{x ^{2} + y ^{2}}{x ^{2} - y ^{2}}

a = \frac{x ^{2} + y ^{2}}{x ^{2} - y ^{2}}, a = - \frac{x ^{2} + y ^{2}}{x ^{2} - y ^{2}}; x^{2} - y^{2} \neq = 0

作图

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