MATH SOLVE

3 months ago

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

Accepted Solution

A:

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]

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]