# a circle has its centre at the origin and a radius of root 12 .state wether each of the following point is on,outside or inside the circle(1,-root 17),(3,5),(2,2root 2)

Consider the figure,

1) Here, we need to find that the point $\left(1,-\sqrt{17}\right)$lie inside the circle, on the circle or outside it.
For this, use the distance formula; ${r}^{2}={\left({x}_{2}-{x}_{1}\right)}^{2}+{\left({y}_{2}-{y}_{1}\right)}^{2}$.
Here, calculate the distance between the origin and the point $\left(1,-\sqrt{17}\right)$. So,
${x}_{1}=0\phantom{\rule{0ex}{0ex}}{x}_{2}=1\phantom{\rule{0ex}{0ex}}{y}_{1}=0\phantom{\rule{0ex}{0ex}}{y}_{2}=-\sqrt{17}$
Substituting the above values in the distance formula, we get

As, ${r}_{1}>r$, so point $\left(1,-\sqrt{17}\right)$lies outside the circle.
2) Here, we need to find that the point $\left(3,5\right)$lie inside the circle, on the circle or outside it.
For this, use the distance formula; ${r}^{2}={\left({x}_{2}-{x}_{1}\right)}^{2}+{\left({y}_{2}-{y}_{1}\right)}^{2}$.
Here, calculate the distance between the origin and the point $\left(3,5\right)$. So,
${x}_{1}=0\phantom{\rule{0ex}{0ex}}{x}_{2}=3\phantom{\rule{0ex}{0ex}}{y}_{1}=0\phantom{\rule{0ex}{0ex}}{y}_{2}=5$
Substituting the above values in the distance formula, we get

As, ${r}_{2}>r$, so point $\left(3,5\right)$lies outside the circle.
3) Here, we need to find that the point $\left(2,2\sqrt{2}\right)$lie inside the circle, on the circle or outside it.
For this, use the distance formula; ${r}^{2}={\left({x}_{2}-{x}_{1}\right)}^{2}+{\left({y}_{2}-{y}_{1}\right)}^{2}$.
Here, calculate the distance between the origin and the point $\left(2,2\sqrt{2}\right)$. So,
${x}_{1}=0\phantom{\rule{0ex}{0ex}}{x}_{2}=2\phantom{\rule{0ex}{0ex}}{y}_{1}=0\phantom{\rule{0ex}{0ex}}{y}_{2}=2\sqrt{2}$
Substituting the above values in the distance formula, we get

As, ${r}_{3}=r$, so point $\left(2,2\sqrt{2}\right)$lies on the circle.

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