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