A coaxial system is a family of circles with the same radical axis. Its limiting points are the zero-radius point circles in the family. If the origin is one limiting point for a coaxial system contai

Question

A coaxial system is a family of circles with the same radical axis. Its limiting points are the zero-radius point circles in the family. If the origin is one limiting point for a coaxial system containing x 2 + y 2 − 2 αx − 2 β y + c = 0 , find its other limiting point.

TestHub · Accepted Answer

The pencil with the origin point-circle is x 2 + y 2 − 2 αx / ( 1 + t ) − 2 β y / ( 1 + t ) + c / ( 1 + t ) = 0 . The non-origin zero-radius member has 1 + t = ( α 2 + β 2 ) / c and centre ( c α , c β ) / ( α 2 + β 2 ) . This requires nonzero denominator and appropriate real limiting configuration.

Mathematics - Circle Question with Solution | TestHub

Options:

Doubts & Discussion