Question

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

Answer 1

no overlap

Explanation:

What we have to do here is compare the distance (d) between the centres with the 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 points"`

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

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

`=sqrt34 ≈ 5.83`

radius of A + radius of B = 3 + 1 = 4

Since sum of radii < d , then no overlap
graph{(y^2-4y+x^2+8x+11)(y^2+2y+x^2-2x+1)=0 [-10, 10, -5, 5]}