Find the condition for the following set of curves to intersect orthogonally: `(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.`

Explanation

1)`(2x)/a^2+(2y)/b^2-dy/dx=0`

`m_1=dy/dx=(-b^2x)/(a^2y)`

`(2x)/A^2-(2y)/B^2*dy/dx=0`

`m_2=dy/dx=(B^2x)/(A^2y)`

`m_1*m_2=-1`

`b^2/a^2*x/y*B^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`

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