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# Does the point $(-2.5,3.5)$ lie inside, outside or on the circle $x^2+y^2=25$?

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• Given C (h, k) be the centre and r the radius of circle. Let P(x, y) be any point on the circle. Then, by the definition, | CP | = r . By the distance formula, we have, $(x-h)^2+(y-k)^2=r^2$
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Given the circle $x^2+y^2 = 25 \rightarrow r = \sqrt {25} = 5$ and $h=0$ and $k=0$
Given the point $(-2.5,3.5)$, we can calculate the distance between that point and the centre of the circle $(0.0)$ as follows:
$\Rightarrow d = \sqrt{ (-2.5-0)^2 + (3.5-0)^2} = \sqrt {6.25+12.25} = \sqrt {18.5} \approx 4.3$
Now $d = 4.3 \lt r = 5 \rightarrow$ point lies inside the circle.
edited Apr 1, 2014