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

Options

A. rectangle
B. trapezium
C. rhombus
D. None of these

Answer

C

Explanation

The equation of the straight lines represented by the two equations `y-mx=+-asqrt(1+m^2) and y-nx=+-a(1+n^2)` 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 from a parallelogram. Also , the distance between the lines (i) and (ii) is same as the distance between the lines (iii) and (iv) each equal to `2|a|`.
So, the given lines from a rhombus.