If the equation `lambdax^2+2y^2-5xy+5x-7y+3=0` represents two straight lines , then the value of `lambda` will be

Options

A. 3
B. 2
C. 8
D. -8

Answer

B

Explanation

We have , `lambdax^2+2y^2-5xy+5x-7y+3=0`.....(i)
Since Eq.(i) represents two straight lines
`therefore|{:(lambda,-(5)/(2),(5)/(2)),(-(5)/(2)," "2,-(7)/(2)),((5)/(2),-(7)/(2),3):}|=0`
`rArr lambda(6-(49)/(4))+(5)/(2)(-(15)/(2)+(35)/(4))+(5)/(2)((35)/(4)-(10)/(2))=0`
`rArr lambda ((24-49)/(4))+(5)/(2)((-30+35)/(4))+(5)/(2)((35-20)/(4))=0`
`rArr -lambda(25)/(4)+(25)/(8)+(75)/(8)=0`
`rArr -(25)/(4)lambda=-(100)/(8)`
`therefore 25lambda=50rArr lambda =2`