Question

Find the combined equation of the following pairs of lines:

Passing through (2, 3) and parallel to the co-ordinate axes.

Answer 1

Equations of the coordinate axes are x = 0 and y = 0.

∴ the equations of the lines passing through (2, 3) and parallel to the coordinate axes are x = 2 and

i.e. x – 2 = 0 and y – 3 = 0.

∴ their combined equation is

(x – 2)(y – 3) = 0. 

∴ xy – 3x – 2y + 6 = 0.