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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
8 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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Askiitians Experts

8 years ago
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