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

Hi OrangeJuice.

Welcome to our web2.0calc forum  laugh


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)


3) subrtact the 2 radii.


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.



Please no one race in with a final answer.  Teaching answers are usually best.

 Jul 30, 2021
edited by Melody  Jul 30, 2021

Hi, it looks like your support is really helpful!

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

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



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



 Jul 30, 2021

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

23 Online Users