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two points P&Q are given.R is variable point on one side of line PQ such that /_RPQ-/_RQP(angle RPQ minus angle RQP) is positive constant 2A. Find locus of R.
The answer is given as x2+y2+2ayCot(2A)=a2
Plz explain.
Hi Karthik,
If the locatio of the P and Q are given on the coordinate axis then only we can get the desired answer.x2+y2+2ayCot(2A)=a2
To solve this problem...
Let us consider P at (0,0) and Q(a,0)
Let angle at Q be Θ then angle at P is Θ+2A
slope of QR is -tanΘ and slope of PR is tan(Θ+2A)
equation of QR is y= -tanΘ(x-a) and PR is y= tan(Θ+2A) x
Consider R(x1,y1) and satisfies QR and PR equations.
y1 =-tanΘ(x1-a) and y1= tan(Θ+2A) x
substituting tanΘ = y1/(a-x1) in y1= tan(Θ+2A) x we get a equation in x1 and y1.
substituting (x1,y1) with (x,y) we get the locus of R
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