If a linear equation has solutions (-2,2)(0,0) and (2,-2), then it is of the form

Options

A. y-x=0
B. x+y=0
C. `-2x+y=0`
D. `-x+2y=0`

Answer

B

Explanation

Let us consider a linear equation ax+by+c=0
Since, `(-2),2)`, (0,0) and (2,-2) are the solutions of linear equation therefore it satisfies the Eq. (i), we get
At point `(-2),2), " " -2a+2b+c=0`
At point `(0,0), " " 0+0+c=0 implies c=0`
and at point `(2,-2), " " 2a-2b+c=0`
From Eqs. (ii) and (iii),
c=0 and `-2a+2b+0=0, -2a=-2b,a=(2b)/(2) implies a=b`
On putting a=b and c=0 in Eq. (i),
`bx+by+0=0 implies bx+by=0`
`implies " " b(x+y) =0 implies x+y=0, b ne 0`
Hence, x+y=0 is the required form of the linear equation.