A straight line L is drawn through the point A(2, 1) such that its point of intersection with the straight line x + y = 9 is at a distance of 3√2 from A. Find the angle which the line L makes with the positive direction of the x-axis.
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Step-by-step explanation:
Let the point of intersection be P(h,k)
As P is on x+y=9
⇒k=9−h
⇒P(h,9−h)
Given, PA=3
2
⇒
(h−2)
2
+(g−h−1)
2
=3
2
⇒(h−2)
2
+(h−8)
2
=18
⇒2h
2
−20h+50=0
⇒h
2
−10h+25=0
⇒(h−5)
2
=0
⇒h=5⇒k=4
⇒L passes through (5,4) and (2,1)
⇒ Slope =
5−2
4−1
=
3
3
=1
⇒tanθ=1
⇒θ=
4
π
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