Question

What loci are represented by the equations :
$(x+y{)}^2-c^2=0.$

Answer 1

${(x+y)}^2-c^2=0$

Factorising the equation

$(x+y+c)(x+y-c)=0x+y+c=0,x+y-c=0$

Slopes of both the lines is same

Hence the equation represents a pair of parallel straight lines.