If the lines `x^2+2x y-35 y^2-4x+44 y-12=0 and 5x+lambday-8` are concurrent, then the value of `lambda` is

Options

A. 0
B. 1
C. -1
D. 2

Answer

D

Explanation

Given line is `x^2+2xy-35y^2-4x+44y-12=0`
Here, `a=1,b=-35,c=-12,h=1,g=-2,f=22`
`therefore` Point of intersection
`=((bg-hf)/(h^2-ab),(af-gh)/(h^2-ab))=((70-22)/(1+35),(22+2)/(1+35))=((4)/(3),(2)/(3))`
If the lines are concurrent , then point `((4)/(3),(2)/(3))` will be on the line `5x+lambday-8=0`.
`therefore 5((4)/(3))+lambda((2)/(3))-8=0`
`rArr (2)/(3)lambda=8-(20)/(3)=(4)/(3)rArr lambda=2`