Let θ be the angle formed by the required direction with the positive direction of x-axis, then the equation of line passes through a point (–1, 2) and in the positive direction is

x−(−1)

cosθ

=

y−2

sinθ

= a
Clearly |a| is the distance of (x, y) from (–1, 2).
Any point on this line is (x, y) = (a cosθ – 1, a sinθ + 2)
Since

x+1

cosθ

= a ⇒ x = a cos θ - 1 and

y−2

sinθ

= a ⇒ y = a sin θ + 2
We have given that when this point lies on x + y = 4, then |a| = 3,
∴ a cosθ – 1 + a sinθ + 2 = 4, |a| = 3
⇒ a (cos θ + sin θ) = 3 , a2 = 9 ⇒ (cosθ+sinθ)2 =

9

a2

,a2 = 9
⇒ cos2θ+sin2θ + 2 sin θ cos θ =

9

9

= 1
⇒ 1 + sin2θ = 1 ⇒ sin2θ = 0 ⇒ 2θ = 0° or 180° ⇒ θ = 0° or 90°
Hence the required line is either parallel to x-axis or parallel to y-axis.