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This circle is centered at the origin, and the length of its radius is 4. What is the equation of the circle?

A. [tex]\((x-4)^2 + (y-4)^2 = 16\)[/tex]

B. [tex]\(x^2 + y^2 = 4^2\)[/tex]

C. [tex]\(\frac{x^2}{4} + \frac{y^2}{4} = 1\)[/tex]

D. [tex]\(x^2 + y^2 = 4\)[/tex]

Sagot :

GinnyAnsweridn
To find the equation of a circle centered at the origin with a given radius, we use the standard form of the equation for a circle.

The standard form of the equation of a circle with center [tex]$(h, k)$[/tex] and radius [tex]$r$[/tex] is:
[tex]$(x - h)^2 + (y - k)^2 = r^2.$[/tex]

In this case, the circle is centered at the origin, so the center [tex]$(h, k)$[/tex] is [tex]$(0, 0)$[/tex]. Therefore, the equation simplifies to:
[tex]$(x - 0)^2 + (y - 0)^2 = r^2.$[/tex]

This further simplifies to:
[tex]$x^2 + y^2 = r^2.$[/tex]

Given that the radius [tex]$r$[/tex] is 4, we substitute [tex]$r = 4$[/tex] into the equation:
[tex]$x^2 + y^2 = 4^2.$[/tex]

Thus, the equation of the circle centered at the origin with a radius of 4 is:
[tex]$x^2 + y^2 = 4^2.$[/tex]

Therefore, the correct answer is:
B. [tex]$x^2 + y^2 = 4^2$[/tex]
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