The condition for the coaxial system x^2+y^2+ | vedclass

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(D) The general equation of a coaxial system of circles is given by $x^2+y^2+2\lambda x+c=0$. Limiting points are the centers of the circles of radius

Vedclass · Accepted Answer

$c>0$

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(D) The general equation of a coaxial system of circles is given by $x^2+y^2+2\lambda x+c=0$. Limiting points are the centers of the circles of radius zero in the system. Setting the radius $r = \sqrt{g^2+f^2-c} = 0$,we get $\sqrt{\lambda^2-c} = 0$,which implies $\lambda^2 = c$. For the limiting points to be distinct and real,we must have $\lambda^2 > 0$,which implies $c > 0$. Thus,the condition for the system to have distinct limiting points is $c > 0$.

The condition for the coaxial system $x^2+y^2+2\lambda x+c=0$,where $\lambda$ is a parameter and $c$ is a constant,to have distinct limiting points,is

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