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The length of chord of contact of the tangents drawn from the point (2 ,5) to the parabola y^2=8x is

Q .       T h e   l e n g t h   o f   c h o r d   o f   c o n t a c t   o f   t h e   tan g e n t s   d r a w n   f r o m   t h e   p o i n t   ( 2 ,   5 )   t o   t h e   p a r a b o l a   y 2   =   8 x   ,   i s ( a )   1 2   41                                                                 ( b )   41 ( c )   3 2   41                                                                   ( d )   2 41                

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  • 3
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hope so answer is D
  • -17
Answer is c
  • -15
use the parametric form of the parabola, x = at^2 , y = 2at,
from given parabola, we have a = 2
therefore, x = 2t^2 , y = 4t
so
the equation of tangent  at (2t^2 ,4t) is ty = x + 2t^2
now it passes through (2,5)
therefore 
5t = 2 + 2t^2
2t^2 - 5t + 2= 0
solving this we have t1  = 2 , t2 = 1/2
Now , the length of the chord = sqrt ( (t1
  • 2
use the parametric form of the parabola, x = at^2 , y = 2at,
from given parabola, we have a = 2
therefore, x = 2t^2 , y = 4t
so
the equation of tangent  at (2t^2 ,4t) is ty = x + 2t^2
now it passes through (2,5)
therefore 
5t = 2 + 2t^2
2t^2 - 5t + 2= 0
solving this we have t1  = 2 , t2 = 1/2
Now , the length of the chord = sqrt ( (t1^2 - t2^2)+(2t1 - 2t2)^2
apply t1 and t2 value ,then
=(sqrt(369)/4) = 3/4 sqrt(41). 
there answer : 3/4(sqrt(41))
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