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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

6 years ago


Answers : (1)

Hello student,
please find the answer to your question below
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- 4ah2 ( k12-k22)/4a= h1- h2
so length of chord = √[(h1-h2)2 +(k1-k2)2 ]
put the above value u will get length = (y12 -4ax1)(y12 +4a2)/a
2 years ago

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