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92. Let P and Q be any two points on the...

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 these

A

`4x^(2)-9y^(2)+15=0`

B

`4x^(2)-9y^(2)-30=0`

C

`9x^(2)-4y^(2)-30=0`

D

`4x^(2)+9y^(2)-30=0`

Text Solution

Verified by Experts

The correct Answer is:
B
We have, Area `(DeltaOPQ)=(1)/(2)|(0,0,1),(a,(2a)/(3),1),(b,(-2b)/(3),1)|=5` (Given)
`implies(4ab)/(3)=pm10`
So, `4ab=pm30" "......(i)`
Aslo `2h=a+b" "......(ii)`
and `2k=(2a-2b)/(3)impliesa-b=3k" "....(iii)`
As `4ab=(a+b)^(2)-(a-b)^(2)impliespm30=4h^(2)-9k^(2)" "` [Using (i), (ii) and (iii)]
So required locus is `4x^(2)-9y^(2)=pm30`
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