The equation `ax^2+by^2+cx+cy=0 c !-=0` represents a pair of straight lines if

Options

A. `a+b=0`
B. `a+c=0`
C. `b+c=0`
D. None of these

Answer

A

Explanation

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-(c)/(4))=0`
`rArr -(ac^2)/(4)-(bc^2)/(4)=0rArr (c^2)/(4)(a+b)=0`
`therefore a+b=0`