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jauneet singh Grade: 12
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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```
7 years ago

## Answers : (1)

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

Please feel free to post as many doubts on our discussion forum as you can.If you find any question Difficult to understand - post it here and we will get you the answer and detailed  solution very  quickly. We are all IITians and here to help you in your IIT JEE preparation.All the best. Regards,Askiitians ExpertsBadiuddin
```
7 years ago
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