If `lambdax^(2)-10xy+12y^(2)+5x-16y-3=0`, represents a pair of straight lines, then the value of `lambda` is

Options

A. 1
B. -1
C. 2
D. -2

Answer

C

Explanation

On comparing the given line with `ax^2+2hxy+by^2+2gx+2fy+c=0`, we get
`a=lambda, h=-5,b=12,g=(5)/(2),f=-8,c=-3`
It represents a pair of straight line , if
`lambdaxx12xx(-3)+2(-8)((5)/(2))(-5)-lambda(-8)^2-12((5)/(2))^2+3(-5)^2=0`
`rArr -36lambda+200-64lambda-75+75=0`
`rArr 100 lambda=200rArr lambda=2`