Question 1087375
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<pre>
The first circle has the center at (x,y) = (8,10) and the radius {{{sqrt(-115 + 64 + 100)}}} = {{{sqrt(49)}}} = 7 (make completing the squares).


The second circle has the center at (x,y) = (-4,5) and the radius {{{sqrt(-5 + 16 + 25)}}} = {{{sqrt(36)}}} = 6 (do the same).


The distance between the centers is {{{sqrt((8-(-4))^2+(10-5)^2)}}} = {{{sqrt(144 + 25)}}} = {{{sqrt(169)}}} = 13 = 7 + 6, 

exactly as the sum of the radii.


So, we have external touching in this case.
</pre>

Solved.



On using completing the squares to transform a general equation of a circle to its standard form see the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Standard-equation-of-a-circle.lesson>Standard equation of a circle</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Find-the-equation-of-the-circle-given-by-its-center-and-tauching-a-given-line.lesson>Find the standard equation of a circle</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/General-equation-of-a-circle.lesson>General equation of a circle</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Transform-general-eqn-of-a-circle-to-the-standard-form-by-completing-the-squares.lesson>Transform general equation of a circle to the standard form by completing the squares</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Identify-elements-of-a-circle-given-by-its-general-equation.lesson>Identify elements of a circle given by its general equation</A> 

in this site.



Also, &nbsp;you have this free of charge online textbook in ALGEBRA-II in this site

&nbsp;&nbsp;&nbsp;&nbsp;<A HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this online textbook under the topic 
"<U>Conic sections: Ellipses. Definition, major elements and properties. Solved problems</U>".