Circle And System Of Circles Question 262
Question: In the co-axial system of circle $ x^{2}+y^{2}+2gx+c=0 $ , where g is a parameter, if $ c>0 $ then the circles are
[Karnataka CET 1999]
Options:
A) Orthogonal
B) Touching type
C) Intersecting type
D) Non-intersecting type
Show Answer
Answer:
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.
BETA
