If a circle with centre C(alpha ,beta) intersects a rectangular hyperbola with centre L(h,k) at four points P(x1,y1), Q(x2,y2), R(x3,y3) and S(x4,y4), then the maen of the 4 pts P,Q,R,S is the mean of the pts C and L.In other words, the mid-pt of CL coincides with the mean point of P,Q,R,S. Analytically,
(x1+x2+x3+x4)/4 = (alpha +h)/2 , (y1+y2+y3+y4)/4= (beta + k)/2.
1. Five pts are selected on a circle of radius a. The centres of the rectangular hyperbola, each passing through tfour of these points lie on a circle of radius:
A)a B)2a C) a/√2 D)a/2
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2 Answers
1This is a pretty familiar question to me . The original question is from S L Loney , and the answer is the radius must be " a2 " from what I can remember . Though I am unable to post the solution right now , I ' ll definitely do it tomorrow .
11Ricky ne aj tak iska soln post nehi kiya.
Anyone interested, though JEE is over..