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This circle is centered at the origin, and the length of its radius is 6. What is the circle's equation?

A. [tex] x^2 + y^2 = 6 [/tex]
B. [tex] x + y = 36 [/tex]
C. [tex] x^2 + y^2 = 36 [/tex]
D. [tex] x^6 + y^6 = 1 [/tex]

Sagot :

GinnyAnsweridn
To solve for the equation of the circle centered at the origin with a given radius, we need to recall the general form of the equation of a circle. The general equation for a circle centered at the origin [tex]\((0,0)\)[/tex] with radius [tex]\(r\)[/tex] is given by:

[tex]\[ x^2 + y^2 = r^2 \][/tex]

Here, the radius [tex]\(r\)[/tex] is given as 6. We need to substitute [tex]\(r = 6\)[/tex] into the general equation.

First, square the radius:
[tex]\[ r^2 = 6^2 = 36 \][/tex]

Then substitute [tex]\(r^2 = 36\)[/tex] into the equation of the circle:
[tex]\[ x^2 + y^2 = 36 \][/tex]

Thus, the equation of the circle is:
[tex]\[ x^2 + y^2 = 36 \][/tex]

Among the given options, the correct equation is:
C. [tex]\( x^2 + y^2 = 36 \)[/tex]
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