A Straight Line Drawn Through Point A (2, 1) Making An Angle π/4 With The +X-axis Intersects Another Line x + 2y + 1= 0 In Point B. Find The Length AB.

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A straight line drawn through point A (2, 1) making an angle π/4 with the +X-axis intersects another line x + 2y + 1= 0 in point B. Find the length AB.


Correct option is

Let AB = r  

From parametric form, the point B can be taken as:




As B lies on x + 2y + 1= 0, we have:    


Note that r is negative, as the point B lies below the point A.  



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           (x + y – 1) + λ (2x + 3y – 5) = 0

and   (3x + 2y – 4) + µ (x + 2y – 6) = 0  

equation of a straight line that belongs to both the families is:


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(m2, 2m), (mm’m + m’) and (m’2, 2m’)

respectively on the line  



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