The value of `lambda` with `|lambda| lt 16` such that `2x^(2) - 10xy +12y^(2) +5x +lambda y - 3 = 0` represents a pair of straight lines is

Options

A. `-10`
B. `-9`
C. 10
D. 9

Answer

B

Explanation

Given equation is
`2x^(2)- 10 xy +12y^(2) +5x +lambda y -3 = 0`
Here, `a= 2, h =- 5, b = 12, g = (5)/(2), f = (lambda)/(2), c =- 3`
For pair of lines `|{:(a,h,g),(h,b,f),(g,f,c):}| =0`
`rArr |{:(2,-5,5//2),(-5,12,lambda//2),(5//2,lambda//2,-3):}| =0`
`rArr lambda^(2) +25 lambda +144 = 0`
`rArr lambda =- 9`