Which point is on the circle centered at the origin with a radius of 5 units? Distance formula:  (2, )   (2, ) (2, 1) (2, 3)

ANSWER

The point is
[tex](2, \sqrt{21} )[/tex]


EXPLANATION

The formula for finding the equation of a circle with centre,
[tex](a,b)[/tex]

and radius
[tex]r[/tex]
is given by

[tex] {(x - a)}^{2} + {(y - b)}^{2} = {r}^{2} [/tex]


The origin has coordinates
[tex](0,0)[/tex]


The equation of a circle centered at the origin with radius 5 units has equation

[tex] {x}^{2} + {y}^{2} = {5}^{2} [/tex]



or

[tex] {x}^{2} + {y}^{2} = 25[/tex]


When
[tex]x = 2[/tex]
Then we have,

[tex] {2}^{2} + {y}^{2} = 25[/tex]


This implies that,

[tex] 4 + {y}^{2} = 25[/tex]


[tex] {y}^{2} = 25 - 4[/tex]


[tex] {y}^{2} = 21[/tex]


[tex]y = \sqrt{21} [/tex]