The straight lines represented by `(y-m x)^2=a^2(1+m^2)` and `(y-n x)^2=a^2(1+n^2)` from a rectangle (b) rhombus trapezium (d) none of these

Options

A. ractangle
B. trapezium
C. rhombus
D. none of these

Answer

C

Explanation

The equations of the straight lines represebted by the two equations are
`{:(y=mx+asqrt(1+m^(2))" ...(i) "y=mx-asqrt(1+m^(2))" ...(ii)"),(y-nx+asqrt(1+n^(2))" ...(iii) "y-nx-asqrt(1+n^(2))" ...(iv)"):}`
Clearly, we have two sets of parallel straight lines. So, they form a parallelogram. Also, the distance between (i) and (ii) is same as the distance between (iii) and (iv) each equal to `2|a|`.
So, the given lines form a rhombus.