Assume that there is no gravity then a projectile thrown at an angle of 45 degree with the horizontal means....

Without gravity, a projectile launched at 45° has equal initial horizontal and vertical velocity components (vx = v₀cos45°, vy = v₀sin45°). With no acceleration, both components remain constant and equal, so x = y at all times. This gives x - y = 0 as the equation of the straight-line path in the x-y plane. The motion is linear, not circular, and x + y = 0 would mean x = -y, which is incorrect.