Question

i) The coaxial system $x^2+y^2+2\lambda x+5=0$ is a non intersecting system.
ii) The coaxial system $x^2+y^2+4\lambda x-3=0$ is an intersecting system.
Which of the above statements is(are) correct?

• A. Only i
• B. Only ii
• C. Both i & ii
• D. Neither i nor ii

Answer 1

Answer: (C)

Both i & ii

i) $x^2+y^2+2\lambda x+5=0$
So, radical axis of given coaxial system is $s_1-s_2=0$
$x=0$
radius of circle $=\sqrt{{\lambda }^2-5}$
when, $\lambda =\sqrt{5}or-\sqrt{5}$
$x^2+y^2+2\lambda x+5=0$ represent point circle, So,
this system of circle is non-intersecting
ii) $x^2+y^2+4\lambda x-3=0$
radical axis is $x=0$
radius of circle$=\sqrt{4{\lambda }^2+3}>o$
So,
this is system of of intersecting circles.