p is a point on the parabola y²=4x and A is the point (4,0). Q divides Ap in the ratio 1:2. Find the equation of the locus of Q
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if p is any point on the parabola then then co ordinates of p are ( t square , 2t)
{note:- parametric eq of simple par. y sq. = 4ax is x= atsq. and y = 2at }
let points of Q are be x' and y'
then using section formula .
A(4,0)______Q(x',y')__________p(t sq, 2t )
1 2
x'=t sq.+ 8\3 and y'=2t\3
now put value of t from y' in x' to replace t from x' because we have to replace arbitary constants.
therefore 3x'=(3y'\2) sq. +8
solving ,we get [ 9y' sq. -12 x' +32 =0 ] the desired locus of Q note that locus of Q is also a parabola
{note:- parametric eq of simple par. y sq. = 4ax is x= atsq. and y = 2at }
let points of Q are be x' and y'
then using section formula .
A(4,0)______Q(x',y')__________p(t sq, 2t )
1 2
x'=t sq.+ 8\3 and y'=2t\3
now put value of t from y' in x' to replace t from x' because we have to replace arbitary constants.
therefore 3x'=(3y'\2) sq. +8
solving ,we get [ 9y' sq. -12 x' +32 =0 ] the desired locus of Q note that locus of Q is also a parabola
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thats tough