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.

OrangeJuicy Jul 30, 2021

#1**+2 **

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)

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.

Melody Jul 30, 2021

#2**-5 **

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

#4**0 **

OrangeJuice,

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

Melody Jul 30, 2021

#5**-5 **

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