Find the condition for the following set of curves to intersectorthogonally:`(x^2)/(a^2)-(y^2)/(b^2)=1`and `x y=c^2``(x^2)/(a^2)+(y^2)/(b^2)=1`and `(x^2)/(A^2)-(y^2)/(B^2)=1.`

Find the condition for the following set of curves to intersectorthogo

1.	Find the condition for the following set of curves to intersectorthogonally:`(x^2)/(a^2)-(y^2)/(b^2)=1`and `x y=c^2``(x^2)/(a^2)+(y^2)/(b^2)=1`and `(x^2)/(A^2)-(y^2)/(B^2)=1.`
Answer» 1)`(2x)/a^2+(2y)/b^2-dy/dx=0` `m_1=dy/dx=(-b^2x)/(a^2y)` `(2x)/A^2-(2y)/B^2dy/dx=0` `m_2=dy/dx=(B^2x)/(A^2y)` `m_1m_2=-1` `b^2/a^2x/yB^2/A^2*x/y=1` `x^2/y^2=(a^2A^2)/(b^2B^2)` `x^2/a^2+y^2/b^2-x^2/A^2+y^2/B^2=0` `x^2(1/a^2-1/A^2)=-y^2(1/b^2+1/B^2)` `x^2/y^2=-(1/b^2+1/B^2)/(1/a^2-1/A^2)` `(a^2A^2)/(b^2B^2)=-(1/b^2+1/B^2)/(1/a^2-1/A^2)` `a^2A^2(1/a^2-1/A^2)=-b^2B^2(1/b^2+1/B^2)` `a^2A^2((A^2-a^2)/(a^2B^2))=-b^2B^2((B^2+b^2)/(b^2B^2))` `a^2-A^2=b^2+B^2` `a^2-b^2=A^2+B^2`.

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Find the condition for the following set of curves to intersectorthogonally:`(x^2)/(a^2)-(y^2)/(b^2)=1`and `x y=c^2``(x^2)/(a^2)+(y^2)/(b^2)=1`and `(x^2)/(A^2)-(y^2)/(B^2)=1.`

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