InterviewSolution
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InterviewSolution
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92. Let P and Q be any two points on the lines represented by 2x-3y = 0 and 2x + 3y = 0 respectively. If the area of triangle OPQ (where O is origin) is 5, then which of the following is not the possible equation of the locus of mid-point of PO? (a) 4x2-9y2 +30 = 0 (b) 4x2-9y2-30 = 0 c) 9x2-4)/2-30=0 (d) none of theseA. `4x^(2) - 9y^(2) +30 = 0`B. `4x^(2) - 9y^(2) - 30 = 0`C. `9x^(2) - 4y^(2) - 30 = 0`D. none of these |
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Answer» Correct Answer - C We have Area `(DeltaOPQ) = (1)/(2) |quad{:(0,0,1),(a,(2a)/(3),1),(b,(-2b)/(3),1):}|=5` (Given) `rArr (4ab)/(3) = +-10` So `4ab = +- 30` (i) Also `2h = a+b` (ii) and `2k = (2a-2b)/(3)`or `a - b =3k` (iii) As `4ab = (a+b)^(2) -(a-b)^(2)` `rArr +- 30 = 4h^(2) - 9k^(2)` [Using (i),(ii) and (iii)] So required locus can be `4x^(2) - 9y^(2) = +30`. |
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