Question

Circle A has a center at `(3 ,-1 )` and a radius of `6`. Circle B has a center at `(-2 ,-4 )` and a radius of `3`. Do the circles overlap? If not, what is the smallest distance between them?

Answer 1

circles overlap.

Explanation:

What we have to do here is compare the distance ( d) between the centres of the circles to the `color(blue)"sum of the radii"`

• If sum of radii > d , then circles overlap

• If sum of radii < d , then no overlap

To calculate d use the `color(blue)"distance formula"`

`color(red)(bar(ul(|color(white)(a/a)color(black)(d=sqrt((x_2-x_1)^2+(y_2-y_1)^2))color(white)(a/a)|)))`
where `(x_1,y_1)" and " (x_2,y_2)" are 2 coordinate points"`

The 2 points here are (3 ,-1) and (-2 ,-4)

let `(x_1,y_1)=(3,-1)" and " (x_2,y_2)=(-2,-4)`

`d=sqrt((-2-3)^2+(-4+1)^2)=sqrt(25+9)≈5.831`

sum of radii = radius of A + radius of B = 6 + 3 = 9

Since sum of radii > d , then the circles overlap
graph{(y^2+2y+x^2-6x-26)(y^2+8y+x^2+4x+11)=0 [-20, 20, -10, 10]}