Q.398. Equation of a line from polar to Cartesian form

Question 398.
Does this equation represents a straight line ?
The equation : 2/r = 3cos ( θ-π/4) + 2sin (θ + π/4).

Answer 398.
3cos(θ - π/4) + 2sin(θ + π/4)
= 3 [cosθ cos(π/4) + sinθ sin(π/4)] + 2 [sinθ cos(π/4) + cosθ sin(π/4)]
= (5/√2) (cosθ + sinθ)

x = r cosθ and y = rsinθ represents a line with r as a constant
=> cosθ = x/r and sinθ = y/r

Plugging in the given eqn.
2/r = (5/√2) (x/r + y/r)
=> x + y = (2√2)/5
which is the equation of a straight line.

Link to YA!