When do the two circles x^{2} + y^{2} = ax an | vedclass

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(A) The centers of the two circles are $C_1(a/2, 0)$ and $C_2(0, 0)$,and their radii are $r_1 = |a|/2$ and $r_2 = c$ respectively.The two circles touc

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$c = |a|$

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(A) The centers of the two circles are $C_1(a/2, 0)$ and $C_2(0, 0)$,and their radii are $r_1 = |a|/2$ and $r_2 = c$ respectively.The two circles touch each other if the distance between their centers $d = C_1C_2$ is equal to the sum or the difference of their radii.$d = \sqrt{(a/2 - 0)^2 + (0 - 0)^2} = |a|/2$.Condition for touching: $d = |r_1 \pm r_2|$.$|a|/2 = | |a|/2 \pm c |$.This implies:$|a|/2 = |a|/2 + c$ or $|a|/2 = | |a|/2 - c |$.From the first case,$c = 0$,which is rejected as $c > 0$.From the second case,$|a|/2 - c = |a|/2$ or $|a|/2 - c = -|a|/2$.$c = 0$ (rejected) or $c = |a|$.Thus,the condition is $c = |a|$.

When do the two circles $x^{2} + y^{2} = ax$ and $x^{2} + y^{2} = c^{2}$ $(c > 0)$ touch each other?

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