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

The distance between two points $(x_{1}, y_{1})$ $(x_1, y_1)$ and $(x_{2}, y_{2})$ $(x_2, y_2)$ can be calculated as
$distance = \sqrt{{(x_{2} - x_{1})}_{2}^{2} + {(y_{2} - y_{1})}_{2}^{2}}$ $"distance" = sqrt((x_2-x_1)^2 + (y_2-y_1)^2)$
(This formula can be derived using the Pythagorean theorem)

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

As $\sqrt{29} \neq 5$ $sqrt(29) != 5$ this means that $(5, - 2)$ $(5, -2)$ 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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