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# help...

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What is the shortest distance between the circles defined by \$x^2-24x +y^2-32y+384=0\$ and \$x^2+24x +y^2+32y+384=0\$? (I already tried but my answer which is \$sqrt(24)\$ appears to be wrong) Can anybody help please.

Jul 30, 2021

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Hi OrangeJuice.

Welcome to our web2.0calc forum

I have no idea how you got sqrt24 but this is what you need to do

1) these are both circles.  So get them into centre-radius form.  Have you done that yet?  What did you get?

2) find the distance between the central points - (you should be able to see that the circles do not overlap)

It fell out nicely for me, with no sqrts in the final answer.  I have not checked my answer though.

If you want more help then please interact with me.  If I am not around I am sure someone else will fill the void.

**

Jul 30, 2021
edited by Melody  Jul 30, 2021
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Step 1 results:

The distance between the central points is sqrt(24^2+32^2) = 40 and subtracting the distances from the center of the circles gives me 32

After I followed your steps, I got 32 as my final answer and it appears to be correct.

P.S. Thanks!

OrangeJuicy  Jul 30, 2021
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Yes that is really good.  I am glad my steps helped.

I assume you rearranged the circle formulas for yourself ?

Here is a pic (which you already know)

Melody  Jul 30, 2021
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OrangeJuice,

I have asked you to clarify something that you wrote on this post.  Thanks

https://web2.0calc.com/questions/number-theory_82500#r1

Jul 30, 2021
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Thanks, and, hopefully my response in the post https://web2.0calc.com/questions/number-theory_82500#r1 will also be clarifying.

OrangeJuicy  Jul 30, 2021