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

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

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Answer 1 · 2016-01-18T02:07:20

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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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

Explanation:

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