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Find the locus of midpoint of all chord of parabola y 2 = 4x which are drawn through the vertex

Find the locus of midpoint of all chord of parabola y2 = 4x which are drawn through the vertex

Grade:12th pass

1 Answers

Chandra Shekhar Mahoviya
24 Points
6 years ago
y2=4ax is the eqn of the parabola 
here a=1
vertex O(0,0)
let P(at2,2at) be a point
let M(p,q) be the mid pt of chord OP 
p = (at2-0)/2 = at2/2.......(ii)
q=(2at-0)/2 = at.........(i)
from (i) t=q/a........(iii)
putting (iii) in eqn (iI)
p=(a/2)*(q/a)2
q2=2ap
y2=2ap
since a=1
y2=2x
 
 
 

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