Two circles have the following equations #(x +8 )^2+(y -6 )^2= 64 # and #(x +4 )^2+(y -3 )^2= 144 #. 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?

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Answer 1 · 2017-12-05T12:23:41

No. Greatest possible distance between a point in one circle
and a point in other circle is #25# unit.

Centre of first circle #(x+8)^2+(y-6)^2=8^2# is #(-8,6)#

and radius is #8# unit .

Centre of second circle #(x+4)^2+(y-3)^2=12^2# is #(-4,3)#

and radius is #12# unit . Distance between their centres is

#d=sqrt((x_1-x_2)^2+(y_1-y_2)^2)=sqrt((-8+4)^2+(6-3)^2) # or

#d=sqrt(16+9)=5# unit. Two circles intersect if, and only if, the

distance between their centers is between the sum #(12+8)=20#

and the difference #(12-8)=4# of their radii. Here #4<5<12#.

So one circle does not contain on other , they intersect at two

points. Greatest possible distance between a point in one circle

and a point in other circle is #d_g=r_1+r_2+d=8+12+5=25#

units. [Ans]