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Megha Animesh Guha
Asked: 2022-11-09T07:27:26+05:30 In:

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) 4×2-9y2 +30 = 0 (b) 4×2-9y2-30 = 0 c) 9×2-4)/2-30=0 (d) none of these
A. `4x^(2) – 9y^(2) +30 = 0`
B. `4x^(2) – 9y^(2) – 30 = 0`
C. `9x^(2) – 4y^(2) – 30 = 0`
D. none of these

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) 4×2-9y2 +30 = 0 (b) 4×2-9y2-30 = 0 c) 9×2-4)/2-30=0 (d) none of these
A. `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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  1. 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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