Two circles have the following equations: #(x +3 )^2+(y -1 )^2= 64 # and #(x -7 )^2+(y +2 )^2= 25 #. 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
One circle does not contain other. Circles intersect each other. Greatest possible distance between point on one circle and another point on the other is
Explanation:
By general:
First let's find the centers and the R of each circle:
For
Center:
For
Center:
The distance between two points given by Protagoras:
The distance between the centers of the circles above given by Protagoras:
We saw that
graph{((x+3)^2+(y-1)^2-64)((x-7)^2+(y+2)^2-25)=0 [-20, 20, -10, 10]}