# Prove or disprove that the point (1, sqrt3) lies on the circle that is centered at the origin and contains the point (0,2)

Prove or disprove that the point (1, $$\sqrt{3}$$) lies on the circle that is centered at the origin and contains the point (0,2)

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Mitchel Aguirre

The standard equation of a circle with center (h,k) and radius r is given by:
$$\displaystyle{\left({x}−{h}\right)}^{{2}}+{\left({y}−{k}\right)}^{{2}}={r}^{{2}}$$
Using $$(h,k)=(0,0)$$ and $$(x,y)=(0,2)$$, we solve for r2:
$$(0-0)2+(2-0)2=r2$$
$$4=r2$$
So, the equation of the circle is:
$$\displaystyle{x}^{{2}}+{y}^{{2}}={4}$$
The point (1,$$\sqrt{3}$$) lies on the circle if it satisfies the equation so we check:
$$\displaystyle{1}^{{2}}+{\left(√{3}\right)}^{{2}}=?{4}$$
$$1+3=?4$$
$$4=4$$
Since it satisfies the equation, then $$\displaystyle{\left({1},√{3}\right)}$$ lies on the circle.