If P (x 1 , y 1 ), Q(x 2 , y 2 ), R(x 3 , y 3 ) and S(x 4 , y 4 ) are four concyclic points on the rectangular hyperbola xy = c 2 , the coordinates of orthocentre of the Δ Δ PQR are:
Text Solution
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Since, points (x r , y r ) is lying on xy = c 2 for r = 1, 2, 3, 4
∴ ∴ 
for r = 1, 2, 3, 4
Slope of QR is - 
.
∴ ∴ Equation of line passing through A and perpendicular to QR is
... (1)
Similarly, equation of line through Q and perpendicular to PR is
... (2)
(1) - (2) ⇒ ⇒ y = 
∴ ∴ 
.
Thus, orthocentre is again lying on xy = c 2 i.e. the fourth point (x 4 , y 4 ).
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