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10-1.Circle and System of Circles
normal
The co-axial system of circles given by ${x^2} + {y^2} + 2gx + c = 0$ for $c < 0$ represents
A
Intersecting circles
B
Non intersecting circles
C
Touching circles
D
Touching or non-intersecting circles
Solution
(a) The equation of a system of circle with its centre on the axis of $x$ is ${x^2} + {y^2} + 2gx + c = 0$.
Any point on the radical axis is $(0,{y_1})$.
Putting $x = 0,\,y = \pm \sqrt { – c} $.
If $c$ is negative $(c < 0)$, we have two real points on radical axis,
then circles are said to be intersecting circles.
Standard 11
Mathematics
