In the xy-plane, the circles with equations (x-3)^2 +y^2=11 and (x+2)^2+y^2=r^2 are externally tangent. what is the value of r? a).3 b)1.3 c)1.7 d)2.8 e)6

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Answer 1 · 2018-03-18T06:33:30

The right option is c) #1.7#.

Let the given circles be,

# S_1 : (x-3)^2+y^2=11, and S_2 : (x+2)^2+y^2=r^2#.

Their respective centres are, #C_1(3,0) and C_2(-2,0)#, and

radii #r_1=sqrt11~~3.3, and r_2=r#.

Given that #S_1 & S_2# touch each other externally, we must have

#" distance "C_1C_2=r_1+r_2#.

#:. sqrt11+r=|3-(-2)|#.

#:. 3.3+r=5, or, r=1.7#.

Hence, the right option is c) #1.7#.