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The straight lines represented by x^2+m ...

The straight lines represented by `x^2+m x y-2y^2+3y-1=0` meet at `(-1/3,2/3)` (b) `(-1/3,-2/3)` `(1/3,2/3)` (d) none of these

A

`(-1//3,2//3)`

B

`(-1//3,-2//3)`

C

`(-1//3,-2//3)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
1, 3
The equation represents a pair of straight lines . Hence,
`1xx(-2)(-1)+2((3)/(2))xx0xx(m)/(2)-1xx((3)/(2))^(2)-(-2)xx0^(2)-(-1)xx((m)/(2))^(2)=0`
or `m=1,-1`
The point of intersection of the pair of lines are obtained by solving
`(partialS)/(partial x)-=2x+my=0and (partialS)/(partialy)-=mx-4y+3=0`
When `m=1`, the required point is the intersection of `2x+y=0,x-4y+3=0` When `m=-1`, the reqired point is the intersection of `2x-y=0,-x4y+3=0`.
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