Question

Assertion (A): The conjugate co-axial system of $x^2+y^2+2\lambda x+c=0$ is
$x^2+y^2+2\mu y-c=0$
Reason (R): the radical axis of given system is perpendicular to the line of centres of conjugate system

• A. Both A and $R$ are True and $R$ is correct explanation of A
• B. Both A and $R$ are True and $R$ is not correct explanation of A
• C. A is True but $R$ is False
• D. A is False but $R$ is True

Answer 1

The correct option is C A is True but $R$ is False

$x^2+y^2+2\lambda x+c=0$
$(x+\lambda {)}^2+y^2+c-{\lambda }^2=0$

$(x+\lambda {)}^2+y^2={\lambda }^2-c$

Therefore the conjugate co-axial circle will be of the form

$x^2+(y+t{)}^2=c-t^2$
Hence the assertion is correct but the reason is incorrect.