+0  
 
+1
88
1
avatar+40 

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.

hatchet288  Aug 31, 2018
 #1
avatar+3277 
+3

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: 

\(17-2.5-7=17-9.5=\boxed{7.5}\).

smileysmiley

tertre  Sep 1, 2018

9 Online Users

avatar

New Privacy Policy

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