Answer:
Option A) [tex](2,\sqrt{21})[/tex]
Step-by-step explanation:
The following information is missing in the question:
A. [tex](2,\sqrt{21})[/tex]
B. [tex](2,\sqrt{23})[/tex]
C. (2, 1)
D. (2, 3)
We are given the following in the question:
A circle centered at origin and radius 5 units.
We have to find the equation of a point that lies on the circle.
Let (x,y) lie on the circle.
Distance formula:
[tex]d = \sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]
Putting
[tex](x_2,y_2) = (x,y)\\(x_1.y_1) = (0,0)\\d = 5[/tex]
We get,
[tex]5 = \sqrt{(y-0)^2 + (x-0)^2}\\\sqrt{x^2+y^2}=5\\x^2+y^2 = 25[/tex]
is the required equation of point on the circle centered at the origin with a radius of 5 units.
The point [tex](2,\sqrt{21})[/tex] satisfies the given equation.
Verification:
[tex](2)^2 + (\sqrt{21})^2\\=4 + 21\\=25[/tex]
Thus, [tex](2,\sqrt{21})[/tex] lies on the circle centered at the origin with a radius of 5 units.
