Two circles have the following equations: #(x +3 )^2+(y -5 )^2= 64 # and #(x -2 )^2+(y +4 )^2= 81 #. Does one circle contain the other? If not, what is the greatest possible distance between a point on one circle and another point on the other?
1 Answer
Aug 27, 2016
No. One circle does not contain the other.
Explanation:
Faced with this problem what can you do?
Sketch it
One circle has centre (-3,5)and radius 8
The other has centre (2,-4) and radius 9
We know this by inspection of the equations..
So draw that line through both centres and out to the circumferences.
How far apart are the centres?
Difference in x coordinates 5, difference in y coordinates 9, from Pythagoras answer
As this is a little over 10 clearly even the centre of the smaller circle is not within the larger.
What is the furthest distance of one circumference from the other?
8 +9+
