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Show that the locus of the point that divides a chord of slope 2 in the ratio 1:2 is a parabola. Find the vertex of the parabola obtained!
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6 Answers
1huh!
assuming the chord is of a std parabola y^2=4ax,
consider two points t1,t2 .. the end points of the chord on the parabola.
slope= 2/t1+t2 =2 => t1+t2=1. ---- #1
consider the reqd point as (h,k) dividing t1,t2 in the ration 1:2.
so we get
h= a/3[t12+2t22] -----#2
k= [2a/3[t1 + 2 t2]] ---------#3
from these three eliminate t1 n t2.
6i am sorry i was not online at that time! anyways thanks for the answers!