Two circles have the following equations #(x -2 )^2+(y -4 )^2= 25 # and #(x +8 )^2+(y +3 )^2= 49 #. 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
Sep 6, 2016
The two circle do not overlap. The greatest possible distance = 24.2066.
Explanation:
Circle A , centered at (2,4), radius = 5.
Circle B, centered at (-8,-3), radius =7.
Distance from center of circle A to center of circle B :
since 12.2066 is greater than the sum of the two radii (5+7=12), the two circle do not overlap.
The greatest possible distance bewteen a point on circle A and a point on circle B equals (radius of circle A + distance between the two centers + radius of circle B), which is :
Hope this helps.