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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



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

Grade:12

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
9 years ago
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 abovve value u will get length = (y12 -4ax1)(y12 +4a2)/a

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