Write the standard form equation of the circle described.
Centered at the origin; diameter: $10$

• A. $x^2+y^2=100$
• B. ${(x-5)}^2+{(y-5)}^2=100$
• C. ${(x-10)}^2+{(y-10)}^2=0$
• D. $x^2+y^2=25$

Answer: (D)

Verified step by step guidance

1. Recall the standard form equation of a circle centered at the origin is given by \(x^2 + y^2 = r^2\), where \(r\) is the radius of the circle.
2. Identify the diameter of the circle from the problem, which is given as 10.
3. Calculate the radius \(r\) by dividing the diameter by 2: \(r = \frac{10}{2}\).
4. Square the radius to find \(r^2\): \(r^2 = \left(\frac{10}{2}\right)^2\).
5. Write the equation of the circle using the radius squared: \(x^2 + y^2 = r^2\).