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jauneet singh Grade: 12
        




what v hav 2 find the length of the chord which is from from the point of contact of the tangents with the curve for any type of curve.explain with parabolla and ellipse
7 years ago

Answers : (1)

Badiuddin askIITians.ismu Expert
147 Points
										

Dear jauneet


suppose we have to find the length of chord of parabola y2 =4ax by the tangents from points (x1,y1)


 so equation of chord of contact   :  yy1 = 2a(x+x1)


now find the point of intersection of chord of contact and given parabola


 y2 =4a(yy1 - 2ax1)/2a


or y2 -2yy1 +4ax1 =0


let point of intersectaion are (h1,k1)  and (h2,k2)


 k1 +k2 = 2y1    and k1k2 = 4ax1


now find k1 -k2 


and we also know that  k12 = 4ah1   and k22 = 4ah2 


   so             k12 -k22 = 4ah1- 4ah1


           (  k12 -k22 )/4a= h1- h1


so length of chord = √[(h1-h2)2 +(k1-k2)2 ]


 put the abovve value u will get   length = (y12 -4ax1)(y12 +4a2)/a




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Badiuddin

7 years ago
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