Two circle {x^2} + {y^2} = ax and {x^2} + {y^ | vedclass

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Question

The centres and radii are

$\left(x-\frac{a}{2}\right)^{2}+y^{2}=\frac{a^{2}}{4}, \quad x^{2}+y^{2}=c^{2}$

Centre $\left(\frac{a}{2}, 0\right)$ a

Vedclass · Accepted Answer

$|a|=c$

Vedclass · Answer

The centres and radii are

$\left(x-\frac{a}{2}ight)^{2}+y^{2}=\frac{a^{2}}{4}, \quad x^{2}+y^{2}=c^{2}$

Centre $\left(\frac{a}{2}, 0ight)$ and $(0,0)$ and radius $=\frac{a}{2}$ and $c$

$\sqrt{\left(\frac{a}{2}ight)^{2}+(0-0)}=|| \frac{a}{2}|\pm c|$

$ \Rightarrow\left|\frac{a}{2}ight|=|| \frac{a}{2}|\pm c|$

$\Rightarrow\left|\frac{a}{2}ight|=c-\left|\frac{a}{2}ight|, \quad 	herefore|a|=c$

Two circle ${x^2} + {y^2} = ax$ and ${x^2} + {y^2} = {c^2}$ touch each other if

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