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The equation ax^2+by^2+cx+cy=0 represent...

The equation `ax^2+by^2+cx+cy=0` represent a pair of straight lines , if

A

`a+b=0`

B

`a+c=0`

C

`b+c=0`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
Te given equation will represent a pair of straight lines, if
`|(A,0,c//2),(0,b,c//2),(c//2,cR2,0)|=0`
`rArr" "-(ac^(2))/(4)-(bc^(2))/(4)=0rArr(c^(2))/(4)(a+b)=0rArra+b" "[becausecne0]`
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Knowledge Check

  • The equation ax+by+c=0 represents a straight line

    A
    for all real numbers a,b and c
    B
    only when `a!=0`
    C
    only where `b!=0`
    D
    only when atleast one a and b is non - zero.

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