For JEE straight lines problems, follow these strategic approaches. First, identify the form of line equation best suited to the given data — this choice alone can reduce computation by 50%. Second, for problems involving "a line through the intersection of two given lines," always use the family of lines L1 + lambda*L2 = 0 rather than finding the intersection first. Third, for reflection and image problems, remember the factor distinction: -1 for foot, -2 for image. Fourth, when the problem asks about a pair of straight lines, first check the Delta condition to confirm it truly represents two lines. Fifth, for locus problems, take a general point on the required locus, express the given geometric condition in terms of its coordinates, and simplify. Sixth, homogenization is used to find the joint equation of lines joining the origin to intersection points of a line with a curve: substitute the line equation $\frac{in the form 1 = (lx + my}{n}$) into the curve equation. Finally, always verify your answer by checking it against the given conditions — substituting the point, verifying the slope, or computing the distance.