Question

Two circles have the following equations `(x -2 )^2+(y -4 )^2= 36` and `(x +8 )^2+(y +3 )^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?

Answer 1

The circles overlap and the greatest distance is `=25.21`

Explanation:

The center of circle `A` is `C_A=(2,4)` and radius `r_A=6`

The center of circle `B` is `C_B=(-8,-3)` and radius `r_B=7`

The distance between the centers is

`C_AC_B=sqrt((10)^2+(7)^2)=sqrt149=12.21`

The sum of the radii is

`R=r_A+r_B=6+7=13`

As,

`R>C_AC_B`, the circles overlap

The greatest distance is `=12.21+6+7=25.21`

graph{((x-2)^2+(y-4)^2-36)((x+8)^2+(y+3)^2-49)(y-4-7/10(x-2))=0 [-32.49, 32.46, -16.24, 16.25]}