solution

angle PRQ=90 degree

using m₁m₂=-1

y-1/x-3*y-5/x-6=-1

on solving we get locus of this point as x²+y²-9x-6y+23=0

 

angle PRQ is 90

so Triangle is right angled

so area is 1/2*base*height

find length of base and height

and using formula and equating with 7 we get another equation of this point as x²+y²-9x-6y-125/2=0

Now the point will be the intersection of these two loci

we see that both circles are concentric and distinct,so no common point

Hence no point.

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