Shortest distance to the circle

Question

Find the shortest distance of the circle x²+y²=9 from the point (4,5).

Answer 1

The shortest distance between the point and the circle is given by:

D = | √(x² + y²) - r |

where (x,y) are the coordinates of a point P and r is the radius of the circle.

Since (x,y) = (4,5) and r = √9 = 3,

D = | √(4² + 5²) - 3 | = | √(41) - 3 | ≈ 3.403