Questions
A line is drawn from the point making an angle with the positive direction of x-axis, to meet the line ax + by + c = 0 at Q. The length of PQ is
a
-aα+bβ+cacosθ+bsinθ
b
aα+bβ+ca2+b2
c
aα+bβ+cacosθ+bsinθ
d
none of these
detailed solution
Correct option is A
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+bsinθTalk to our academic expert!
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