IIT JEE , AIEEE Forum - Mathematics , Analytical Geometry - a rectangular hyperbola whose center is C is cut by any circle of radius r in four points

ankitagg

a rectangular hyperbola whose center is C is cut by any circle of radius r in four points P,Q,R,S.then CP^2+CQ^2+CR^2+CS^2=
a)r^2
b)2r^2
c)3r^2
d)4r^2

pinnacle

D Delhi

ankitagg

please post the solution.your answer is correct.

Conjurer

Assuming C to be 0,0 we get the equations of the rect hyperbola and circle as:

xy = c^2

x^2 + y^2 = r^2

So the points intersect on the perimeter. SO distance squared is 4 times radius squared. Draw diagram and see.

ankitagg

sorry ,couldn't understood.please make it more clear to me .

Conjurer

OK see fig.

akhil_o

yes if the rect hyperbola and circle both are in standard form it sis very easy
xy=c*C
and x^2+y^2=r^2
C=(0,0)
since the centres coincide,
every point on circle has distance r from centre of circle=centre of hyperbola
so obviously all 4 points r at distance square=r^2
so sum=4r^2

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