Equations of parallel and perpendicular lines

(i) The equation to the pair of lines passing through (x1, y1) and parallel to ax2 + 2hxy + by2 = 0 is

a(x – x1)2 + 2h(x – x1)(y – y1) + b(y– y1)2 = 0

(ii) The equation to the pair of lines passing through the origin and perpendicular to ax2 + 2hxy + by2 = 0 is

bx2 – 2hxy + ay2 = 0

(iii) The equation to the pair of lies passing through the point (x1, y1) and perpendicular to ax2 + 2hxy + by2 = 0 is

b(x – x1)2 – 2h(x – x1) (y – y1) + a(y – y1)2 = 0