Find the combined equation of the pair of lines through the point (1, 0) and parallel to the lines represented by `2x^2-x y-y^2=0`

Options

A. `2x^(2)-xy-y^(2)-x+y-1=0`
B. `2y^(2)+xy-x^(2)+2x-y-1=0`
C. `2y^(2)+xy-x^(2)-x-xy+2=0`
D. none of these

Answer

B

Explanation

The combined equation of the pair of lines through the origin and perpendicular to the lines given by
`2x^(2)-xy-y^(2)=0 ` is `2y^(2)+xy-x^(2)=0`.
Shifting the origin at (1, 0), the equations of the required lines are
`2y^(2)+(x-1)y-(x-1)^(2)=0`
or, `2y^(2)+xy-x^(2)+2x-y-1=0`