The center of a circle is at (0,0) and its radius is 5. Does the point (5,-2) lie on the circle?

1 Answer
sente
Jan 18, 2016

No

Explanation:

A circle with center #c# and radius #r# is the locus (collection) of points which are distance #r# from #c#. Thus, given #r# and #c#, we can tell if a point is on the circle by seeing if it is distance #r# from #c#.

The distance between two points #(x_1, y_1)# and #(x_2, y_2)# can be calculated as
#"distance" = sqrt((x_2-x_1)^2 + (y_2-y_1)^2)#
(This formula can be derived using the Pythagorean theorem)

So, the distance between #(0, 0)# and #(5, -2)# is
#sqrt((5-0)^2+(-2-0)^2) = sqrt(25+4) = sqrt(29)#

As #sqrt(29) != 5# this means that #(5, -2)# does not lie on the given circle.

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