The straight lines represented by ${(\mathrm{y}-\mathrm{mx})}^2={\mathrm{a}}^2(1+{\mathrm{m}}^2)$ and ${(\mathrm{y}-\mathrm{nx})}^2={\mathrm{a}}^2(1+{\mathrm{n}}^2)$ form a

detailed solution

Correct option is B

The straight lines represented by (y−mx)2=a2(1+m2) are y−mx=±a1+m2i.e.,y−mx=a1+m2 (1) and y−mx=−a1+m2(2) Similarly, the straight lines represented by (y−nx)2=a2(1+n2) are y−nx=a1+n2(3) and y−nx=−a1+n2 (4) Since the lines (1) and (2) are parallel, the distance between them is |a1+m2+a1+m21+m2|=|2a|Similarly, the lines (3) and (4) are parallel lines and the distance between them is |2a|.Since the distance between parallel lines are the same, the four lines form a rhombus.