Q. 155.0( 2 Votes )

Find the le

Answer :

Given that we need to find the length of the line joining the vertex of parabola y2 = 4ax and a point on the parabola where the line segment makes an angle θ to the x - axis.



We know that vertex of the parabola is (0, 0).


We know that the equation of the line passing through origin and making angle θ to the x - axis is given by y = (tanθ)x.


Substituting y value in the equation of parabola we get,


(xtanθ)2 = 4ax


x2tan2θ = 4ax


xtan2θ = 4a



y = tanθx




The point on the parabola is .


We know that the distance between the two points (x1, y1) and (x2, y2) is .









S = 4a2cotθcosecθ.


The distance is 4a2cotθcosecθ.


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