Two circles have the following equations: #(x -1 )^2+(y -4 )^2= 64 # and #(x +6 )^2+(y -9 )^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?

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Answer 1 · 2017-03-16T09:20:44

#"As "r_r+r_b " is greater than l, one circle contains the other."#

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#"The general Circle equation can be written as the below"#

#(x-a)^2+(y-b)^2=r^2#

#"Where (a,b) center coordinates,r radius of circle."#

#O_b(-6,9) " represents the center of blue circle."#

#O_r(1,4)" represents the center of red circle."#

#r_r:" radius of the red circle ,"r_r=sqrt(64)" , "r_r=8 " units"#

#r_b:" radius of the red blue ,"r_r=sqrt(49)" , "r_b=7 " units"#

#l : "represents distance from "O_r " to "O_b#

#l=sqrt((1+6)^2+(9-4)^2))" , "l=sqrt(7^2+5^2)" , "l=8.6" #

#r_r+r_b=7+8=15#

#l=8.6#

#r_r+r_b >l#

#"As "r_r+r_b " is greater than l, one circle contains the other."#