To find the radius of the circle from its equation, let's carefully follow these steps:
1. Understand the Equation of a Circle:
The standard form of the equation of a circle is [tex]\((x - h)^2 + (y - k)^2 = r^2\)[/tex], where:
- [tex]\((h, k)\)[/tex] is the center of the circle.
- [tex]\(r\)[/tex] is the radius of the circle.
2. Identify the Given Equation:
The given equation is [tex]\(x^2 + y^2 = 64\)[/tex].
3. Compare with the Standard Form:
Comparing this with the standard form [tex]\((x - h)^2 + (y - k)^2 = r^2\)[/tex]:
- We observe that [tex]\(h = 0\)[/tex] and [tex]\(k = 0\)[/tex], indicating the circle is centered at the origin [tex]\((0, 0)\)[/tex].
- The equation simplifies to [tex]\(x^2 + y^2 = r^2\)[/tex].
4. Determine the Value of [tex]\(r^2\)[/tex]:
From the equation [tex]\(x^2 + y^2 = 64\)[/tex], it follows that:
[tex]\[ r^2 = 64 \][/tex]
5. Solve for [tex]\(r\)[/tex]:
To find the radius [tex]\(r\)[/tex], take the square root of both sides:
[tex]\[ r = \sqrt{64} \][/tex]
[tex]\[ r = 8 \][/tex]
6. Conclusion:
Therefore, the radius of the circle is [tex]\(8\)[/tex].
Given the multiple-choice options:
- A. 64
- B. 4
- C. 8
- D. 32
The correct answer is:
[tex]\[ \boxed{8} \][/tex]
