Two circles have the following equations: #(x +6 )^2+(y -1 )^2= 49 # and #(x +4 )^2+(y +7 )^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
t0hierry
Dec 14, 2016

Still working on it. I wanted to give you something to start with. More soon.

Explanation:

The first circle has center #(-6.1)# and radius 7. The second circle has center #(-4,7)# and radius 9.source webmath
The line joining both centers has equation

#y = ax + b# where
#7 - 1 = a(-4 - -6)#
#6 = 2a# or #a=3#

One finds b using

#7 = 3(-4) + b#
or #b=19#

The line given by the above equation

intersects the top circle at point P given by
#(x+4)^2 + (3x + 19-1)^2 = 49#
or #10 x^2 + 8x + 116x + 16 + 18^2 = 49#

The other point on the bottom circle can be found in a similar way.

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