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Two points P(a,0) and Q(-a,0) are given,...

Two points P(a,0) and Q(-a,0) are given, R is a variable on one side of the line PQ such that `/_RPQ-/_RQP` is a positive constant `2alpha`. FInd the locus of point R.

Text Solution

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`/_RPQ=phi`
`/_RQP=theta`
`phi-theta=2alpha`
`tan(phi-theta)=2alpha`
`(tanphi-tantheta)/(1+tanthetatanphi)=tan2alpha`
`tantheta=y/(x+a),tanphi=y/(a-x)`
`(y/(x+a)+y/(x-a))/(1-y^2/((x-a)(x-b)))=tan2alpha`
`(2xy)/(a^2-x^2+y^2)=tan2alpha`.
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