JEE Advance - Mathematics (1998 - No. 26)
If the circle $${x^2}\, + \,{y^2} = \,{a^2}$$ intersects the hyperbola $$xy = {c^2}$$ in four points $$P\,({x_1},\,{y_1}),\,Q\,\,({x_2},\,{y_2}),\,\,R\,({x_3},\,{y_3}),\,S\,({x_4},\,{y_4}),$$ then
$${x_1}\, + \,{x_2} + \,{x_3}\, + \,{x_4}\, = 0$$
$${y_1}\, + \,{y_2} + \,{y_3}\, + \,{y_4}\, = 0$$
$${x_1}\,{x_2}\,{x_3}\,{x_4}\, = {c^4}$$
$${y_1}\,{y_2}\,{y_3}\,{y_4}\, = {c^4}$$
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