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Straight lines (x)/(a)+(y)/(b)=1, (x)/(b)+(y)/(a)=1,(x)/(a)+(y)/(b)=2 and (x)/(b)+(y)/(a)=2 form a rhombus of area ( in squareunits)

Answer»

`(ab)/(|a^(2)-B^(2)|)`
`(ab)/(a^(2)+b^(2))`
`(a^(2)b^(2))/(a^(2)+b^(2))`
`(a^(2)b^(2))/(|a^(2)-b^(2)|)`

Solution :The equationsof the FOUR sides are
`(x)/(a)+(y)/(b)=1""…(i)""(x)/(b)+(y)/(a)=1`
`(x)/(a)+(y)/(b)=2""…(iii) ""(x)/(b)+(y)/(a)=2""…(iv)`
CLEARLY , (i), (iii) and (ii), (iv) FORM two sets of parallel lines. So, the four lines form a parallelogram.
Area of RHOMBUS`=|((2-1)(2-1))/({:((1)/(a),(1)/(b)),((1)/(b),(1)/(a)):})|=|(1)/((1)/(a^(2))-(1)/(b^(2)))|`
`implies` Area of the rhombus `=(a^(2)b^(2))/(|b^(2)-a^(2)|)`


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