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Analytical Geometry

If P(x1,y1), Q(x2, y2),R(x3, y3)&S(x4,y4) are four concyclic points on the rectangular hyperbola xy=c^2, the coordinates of the orthocentre of the triangle PQR areAns(-x4,-y4)Plz give the full solution!!!!!

Profile image of aayushi verma
8 Years agoGrade
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1 Answer

Profile image of Patel Dev Shaileshbhai
7 Years ago
H = xy = c2
(ct , c/t) is the harmonic coordinates 
 
from equation of circle 
 
x2 + y2 + 2gx + 2fy + c/ = 0
then 
 
c2t2 + c2/t2 + 2gct + 2fc/t + c/ = 0
 
-t4  + 2gt3 + 2ft/c + c/t2 + 1 = 0 
 
if t1 t2 t3 t4 on the circle 
then 
 
t1t2t3t4 = – 1 .
 
AND THEN ,
 
t4 = -t4 
 
so , ANS (-x4 ,-y4)
 

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