Question #09598

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Question #09598

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Answer 1 · 2016-05-18T21:34:05

There are three common tangents.

Explanation:

Generally speaking, equation
${(x - a)}^{2} + {(y - b)}^{2} = R^{2}$ $(x-a)^2+(y-b)^2=R^2$
describes a circle of the radius $R$ $R$ with a center at point $O (a, b)$ $O(a,b)$ .

The first equation can be transformed into
$x^{2} + {(y - \frac{1}{2})}^{2} = {(\frac{1}{2})}^{2}$ $x^2+(y-1/2)^2=(1/2)^2$
This equation describes a circle of a radius $\frac{1}{2}$ $1/2$ with a center at point $(0, \frac{1}{2})$ $(0,1/2)$ .

The second equation can be transformed into
$x^{2} + {(y + \frac{1}{2})}^{2} = {(\frac{1}{2})}^{2}$ $x^2+(y+1/2)^2=(1/2)^2$
This equation describes a circle of a radius $\frac{1}{2}$ $1/2$ with a center at point $(0, - \frac{1}{2})$ $(0,-1/2)$ .

Obviously, these two circles are tangential to each other with a common point at $(0, 0)$ $(0,0)$ .
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Question #09598

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