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If one of the lines given by the equatio...

If one of the lines given by the equation `2x^(2)+pxy+3y^(2)=0` coincide with one of those given by `2x^(2)+qxy-3y^(2)=0` and the other lines represented by them are perpendicular , then value of `p+q`is

A

6

B

-6

C

-7

D

7

Text Solution

Verified by Experts

The correct Answer is:
1 ,2
Let `(2)/(3)x^(2)+(p)/(3)xy+y^(2)=(y-mx)(y-m'x)`
and `(2)/(-3)x^(2)+(q)/(-3)xy+y^(2)=(y+(1)/(m)x)(y-m'x)` then ,
`m+m'=-(p)/(3),mm'=(2)/(3)` (1)
`(1)/(m)-m'=(-q)/(3),-(m')/(m)=-(2)/(3)` (2)
or `m^(2)=1orm=+-1`
If `m=1,m'=2//3` and , so , p =-5,q=-1,m'`=-2//3` and , so , p =5 , q =1.
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