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If the lines 3x^(2)-4xy +y^(2) +8x - 2y-...

If the lines `3x^(2)-4xy +y^(2) +8x - 2y- 3 = 0` and `2x - 3y +lambda = 0` are concurrent, then the value of `lambda` is

A

`4pi - 11`

B

`-11`

C

`(1)/(11)`

D

11

Text Solution

Verified by Experts

The correct Answer is:
D
We have `f(x,y) -= 3x^(2) -4xy +y^(2) +8x -2y -3 =0`
Differentiating w.r.t. x keeping y as constant
`(delf)/(delx) = 6x -4y +8 = 0` (i)
Differentiating w.r.t y keeping x ax constant
`(delf)/(dely) =- 4x +2y -2 =0` (ii)
Solving (i) and (ii), the point of intersection of the pair of lines is (2,5).
It satisfies the equation `2x - 3y + lambda = 0`
`rArr lambda = 11`
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