Question

Limiting points of the co-axial system.

Answer 1

Let the circle is x² +y² +2gx+c = 0

Where g is a variable and c is constant

∴centre (–g,0) and radius \(\sqrt{g^2-c}\)

Let \(\sqrt{g^2-c}\) = 0 radius

g² –c = 0

g² = c

g = ± \(\sqrt{c}\)

Thus we get the two limiting points of the given co-axial system as

\((\sqrt{c,},0) \&(-\sqrt{c},0)\)

The limiting points are real and distinct, real and coincident or imaginary according as C>,=, <0.