A line is drawn from the point Pα,β making an angle θ with the positive direction of x-axis, to meet the line ax + by + c = 0 at Q. The length of PQ is

Equation of a straight line passing through the point Pα,β and making an angle θ with positive direction of x-axis isx-αcosθ=y-βsinθ=rsayCoordinates of any point on this line areα+rcosθ,β+rsinθIf it lies on the line ax + by + c = 0, thenaα+rcosθ+bβ+rsinθ+c=0⇒r=-aα+bβ+cacosθ+bsinθThus, PQ=r=-aα+bβ+cacosθ+bsinθ