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(1)A triangle formed by the lines x+y=0 ...

`(1)`A triangle formed by the lines `x+y=0 , x-y=0` and `lx+my=1`. If `l`and `m` vary subject to the condition `l^2+m^2=1` then the locus of the circumcentre of triangle is: `(2)`The line `x +y= p` meets the `x`-axis and `y`-axis at `A` and `B`, respectively. A triangle `APQ` is inscribed in triangle `OAB, O` being the origin, with right angle at `Q. P` and `Q` lie, respectively, on `OB` and `AB`. If the area of triangle `APQ` is `3/8th` of the area of triangle `OAB`, then `(AQ)/(BQ)` is: equal to

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