# Thread: Maxima / Minima - Shortest & Longest distance to a Circles

1. ## 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.

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.
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

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# 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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