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
$(2, \sqrt{21} )$


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,

$4 + {y}^{2} = 25$


${y}^{2} = 25 - 4$


${y}^{2} = 21$


$y = \sqrt{21}$

Answer 2

The answer is (2, sqr root 21). Hope this helps