The figure formed by the pairs of lines 6 x^2+13 x y+6 y^2=0 and 6 x^2+13 x y+6 y^2+10 x+10 y+4=0 , is a

Step-by-step solution

(c) Equation of pair of lines, aligned & 6 x^2+13 x y+6 y^2=0 & 6 x^2+9 x y+4 x y+6 y^2=0 & 3 x(2 x+3 y)+2 y(2 x+3 y)=0 & (3 x+2 y)(2 x+3 y)=0 & 3 x+2 y=0 and 2 x+3 y=0 aligned Similarly, for another equation of pairs of lines 6 x^2+13 x y+6 y^2+10 x+10 y+4=0 are 3 x+2 y+2=0 and 2 x+3 y+2=0 Here, A B is parallel to C D and B C is parallel to A D . A B C D is a parallelogram. But also A B=B C=C D=A D= 2 13 Hence, A B C D is a rhombus. Hence, ABCD is a rhombus.