If the equation `ax^2+by^2+cx+cy=0` represents a pair of straight lines , then

Options

A. `a(b+c)=0`
B. `b(c+a)=0`
C. `c(a+b)=0`
D. `a+b+c=0`

Answer

C

Explanation

We have , `ax^2+by^2+cx+cyw=0` ....(i)
The given equation will represent a pair of straight lines , if `|{:(a,0,(c)/(2)),(0,b,(c)/(2)),((c)/(2),(c)/(2),0):}|=0`
`rArr a(0-(c^2)/(4))+(c)/(2)(0-(bc)/(2))=0`
`rArr -(ac^2)/(4)-(bc^2)/(4)=0`
`rArr -(c^2)/(4)(a+b)=0`
`therefore c^2(a+b)=0rArr c(a+b)=0` .