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The length of the latusrectum of the parabola `2{(x-a)^(2)+(y-a)^(2)}=(x+y)^(2),` isA. 2aB. `2sqrt(2)a`C. 4aD. `sqrt2a` |
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Answer» Correct Answer - B We have `2{(x-a)^(2)+(y-a)^(2)}=(x+y)^(2)` `rArr" "sqrt((x-a)^(2)+(y-a)^(2))=1/sqrt2|x+y|` `rArr" "sqrt((x-a)^(2)+(y-a)^(2))=|(x+y)/sqrt2|` Clerly, this equation represents a parabola having its focus at (a, a) and directrix x + y = 0 `:.` L.R.=2 (Distance between focus and directrix) `rArr" "L.R.=2|(a+a)/(sqrt(1+1))|=2sqrt2a` |
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