When we are given an equation of a pair of straight lines $ax^2+2hxy+by^2+2gx+2fy+c=0$, the homogeneous part of the equation i.e., $ax^2+2hxy+by^2$ gives the angle between the two straight lines constituting the pair. The other terms influence the point of intersection of the pair. When the other terms are zero or the equation consists of only the homogeneous part, it represents a pair of straight lines having the origin as their point of intersection.
On a graph paper, on varying the non-homogeneous part of the entire equation we actually translate the system without rotating it. The new set of lines remain parallel to the original set.
Is it possible to achieve or obtain the equation of pair of straight lines which are perpendicular to another pair of straight lines, under the condition, the new pair of straight lines passes through the origin (for the sake of simplicity, or you may consider an arbitrary point $(p,q)$)? How are the homogeneous part of the original equation and the new equation related? In this case, how would the behaviour of non-homogeneous terms affect our result?