We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.

Hello, here's another problem of the week!

What is the shortest distance, in units, between the circles \((x-9)^2 + (y-5)^2 = 6.25\) and \((x+6)^2 + (y+3)^2 = 49\)? Express your answer as a decimal to the nearest tenth.

 Aug 31, 2018

This is a bit tough, but here's my take!

The shortest distance between two circles, is: \(C_1C_2-r_1-r_2\).


We have \(C_1\) as (9,5) as we take out the negatives from (-9,-5), and the radius is 2.5.


And, we have \(C_2\) as (-6,-3) as we add the negatives from (6,3), and the radius is 7.


Now, we use the distance formula! \(\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\) Plugging in the value we get, 


\(\sqrt{(-6-9)^2+(-3-5)^2}=\sqrt{225+64}=\sqrt{289}=17\). After this, we subtract both radii, to attain: 



 Sep 1, 2018

12 Online Users