Two circles have the following equations #(x -1 )^2+(y -2 )^2= 64 # and #(x +7 )^2+(y -4 )^2= 9 #. 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 · 2018-01-19T14:27:41

Greatest possible distance between a point on one circle and another point on the other is

#color(brown)(D_f = r_1 + D + r_2 = 8 + 8.2462 + 3 = 19.2462)#

Circle 1

#r_1 = sqrt(64) = 8, o_1 (1,2)#

Circle 2

#r_1 = sqrt9 = 3, o_1 (-7, 4)#

Distance between centers #o_1, o_2#

#D = sqrt((-7-1)^2 + (4-2)^2) = 8.2462#

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Since D is greater than both the radii but less than #(r_1 + r_2), one circle doesn’t contain the other but they overlap.

Greatest possible distance between a point on one circle and another point on the other is

#color(brown)(D_f = r_1 + D + r_2 = 8 + 8.2462 + 3 = 19.2462)#