JEE Advance - Mathematics (1989 - No. 22)
If $$\left( {{m_i},{1 \over {{m_i}}}} \right),\,{m_i}\, > \,0,\,i\, = 1,\,2,\,3,\,4$$ are four distinct points on a circle, then show that $${m_1}\,{m_2}\,{m_3}\,{m_4}\, = 1$$
The statement is true because the product of the abscissas and ordinates must equal 1.
The statement is false as the product can be any positive number.
The statement is true because the points lie on a circle, and the product of the m_i values must relate to the circle's equation.
The statement is true because the four points lying on a circle implies that the product of their parameters must be 1 to satisfy a certain geometric relationship.
The statement is conditionally true, dependent on the circle's center and radius.