The co-axial system of circles given by {x^2} | vedclass

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(A) The equation of the system of circles is ${x^2} + {y^2} + 2gx + c = 0$. The radical axis of this system is obtained by subtracting the equations o

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Intersecting circles

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(A) The equation of the system of circles is ${x^2} + {y^2} + 2gx + c = 0$. The radical axis of this system is obtained by subtracting the equations of any two circles in the system,which results in the $y$-axis $(x = 0)$. To find the intersection points of the circles with the radical axis,we substitute $x = 0$ into the equation: ${0^2} + {y^2} + 2g(0) + c = 0$ ${y^2} = -c$ $y = \pm \sqrt{-c}$. Since $c Therefore,the circles intersect the radical axis at two distinct real points $(0, \sqrt{-c})$ and $(0, -\sqrt{-c})$. Hence,the system represents intersecting circles.

The co-axial system of circles given by ${x^2} + {y^2} + 2gx + c = 0$ for $c < 0$ represents

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