A) Orthogonal
B) Touching type
C) Intersecting type
D) Non-intersecting type
Correct Answer: B
Solution :
Given, equation of the circle x2 + y2 + 2gx + c = 0, where c is constant and g represents the parameter of a coaxial system and c > 0. We know that the standard equation of a circle is \[{{x}^{2}}+{{y}^{2}}+2gx+2fy+c=0.\] Comparing the given equation with the standard equation, we get centre \[\equiv (-g,\,0)\] and radius\[\sqrt{{{g}^{2}}-c}\]. Therefore radius becomes zero, when \[{{g}^{2}}-c=0\] or\[g=\pm \sqrt{c}\]. Therefore \[(\sqrt{c},\,0)\] and \[(-\sqrt{c},\,0)\] are the limiting points of the coaxial system of circles. Since c > 0, therefore \[\sqrt{c}\] is real and limiting points are real and distinct. Thus the co-axial system is said to be touching type.
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