Given the circle having the equation x^2 + y^2 = 9, find a.) The shortest distance from point (4,5) to a point on the circle, and b.) The longest distance from the point (4,5) to a point on the circle.

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- February 21st 2007, 08:41 AM^_^Engineer_Adam^_^Maxima / Minima - Shortest & Longest distance to a Circles
Given the circle having the equation x^2 + y^2 = 9, find a.) The shortest distance from point (4,5) to a point on the circle, and b.) The longest distance from the point (4,5) to a point on the circle.

- February 21st 2007, 09:18 AMCaptainBlack
The point (4,5) is a distance sqrt(41) from the origin which is the centre of

the given circle.

The radius of the given circle is 3, thefore the shortest distance is sqrt(41)-3,

and the greatest distance is sqrt(41)+3.

(Draw a diagram to see how this works).

RonL