Question

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 1

ANSWER

The point is

`(2, √(21) )`


Step-by-step explanation

The formula for finding the equation of a circle with centre,

`(a,b)`

and radius

`r`
is given by


`{(x - a)}^(2) + {(y - b)}^(2) = {r}^(2)`


The origin has coordinates

`(0,0)`


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


`{x}^(2) + {y}^(2) = {5}^(2)`



or


`{x}^(2) + {y}^(2) = 25`


When

`x = 2`
Then we have,


`{2}^(2) + {y}^(2) = 25`


This implies that,


`4 + {y}^(2) = 25`



`{y}^(2) = 25 - 4`



`{y}^(2) = 21`



`y = √(21)`