Two circles have the following equations: #(x -1 )^2+(y -2 )^2= 9 # and #(x +6 )^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
The two circles are outside each other i.e. one circle is not contained in the other and greatest distance between a point on one circle and another point on the other is
Explanation:
The center of
and center of
The distance between centers is
=
Hence sum of raadii is
Hence the two circles are outside each other i.e. one circle is not contained in the other.
and greatest distance between a point on one circle and another point on the other is
For details see https://socratic.org/questions/two-circles-have-the-following-equations-x-4-2-y-3-2-9-and-x-4-2-y-1-2-16-does-o
graph{((x-1)^2+(y-2)^2-9)((x+6)^2+(y+2)^2-25)=0 [-2.853, -0.353, -0.085, 1.165]}
graph{((x-1)^2+(y-2)^2-9)((x+6)^2+(y+2)^2-25)=0 [-12.29, 7.71, -5.34, 4.66]}