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# 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 Badiuddin askIITians.ismu Expert
148 Points
11 years ago

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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