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The angle between the tangents drawn from the origin to the parabola y^2=4a(x-a) is?

The angle between the tangents drawn from the origin to the parabola y^2=4a(x-a) is?

Grade:11

1 Answers

kkbisht
90 Points
3 years ago
Dear Student:
It is clear that that the parabola y2=4a(x-a)  has vertex (a,0) and the focus is therefore at  (2a,0). But  Latus rectum is same(=4a)as for  standard parabola y2=4ax. Therefore extermities(end points of latus rectum ) are  (2a,2a)
Now equation of any tangent to a parabola y2=4ax in slope form is y=mx+a/m but our given parabola is y2=4a(x-a) so the equation of tangent to this parabola is y=m(x-a) +a/m  ( by simple  logic of tranformation of coordinates) .As this tangent passes through origin (0,0) therefore we have 0=m(0-a) +a/m =>ma=a/m or m2=1 ( cancelling a as a is not zero)
which implies that m=+-1. so the slopes of the two tangent are 1 and -1 whose product is -1.Therefore the two tangents drawn from origin to the given parabola y2=4a(x-a) are perpendicular. => angle b/w tangents is 90 degree. 
kkbisht

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