Question

Two circles have the following equations `(x +5 )^2+(y +6 )^2= 36` and `(x +2 )^2+(y -1 )^2= 81`. 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

Smaller circle is not contained in larger circle and they intersect each other. The greatest possible distance between a point on one circle and another point on the other will be `22.6158`.

Explanation:

First circle has center as `(-5,-6)` and radius `6` and second circle has center as `(-2,1)` and radius `9`.

Distance between circles of two centers is `sqrt((-2-(-5))^2+(1-(-6))^2` or `sqrt(3^2+7^2)=sqrt(9+49)=sqrt58=7.6158`

As the distance between two circles at `7.6158` is less than the sum of their radii `6+9=15` and more than the difference between them at `9-63`, smaller circle is not contained in larger circle and they intersect each other.

The greatest possible distance between a point on one circle and another point on the other will be `6+9+7.6158=22.6158`.