Question

The joint equation of the pair of lines passing through (2,3) and parallel to the coordinate axes is

1.  xy − 3x − 2y + 6 = 0
2. xy + 3x + 2y + 6 = 0
3. xy = 0
4. xy − 3x − 2y − 6 = 0

Answer 1

Equation of the coordinate axes are x = 0 and y = 0.
The equations of the lines passing through (2, 3) and parallel to coordinate axes are,
x = 2 and y = 3.
i.e. x − 2 = 0 and y − 3 = 0
The joint equation is given as

(x − 2) (y − 3) = 0

xy − 3x − 2y + 6 = 0