The equation of a circle in standard form is given by:

\[
(x - h)^2 + (y - k)^2 = r^2
\]

where \((h, k)\) is the center of the circle and \(r\) is the radius.

Given:
- Center: \((10, -16)\)
- Radius: \(\sqrt{3}\)

Substitute these values into the standard form equation:

\[
(x - 10)^2 + (y - (-16))^2 = (\sqrt{3})^2
\]

Simplify:

\[
(x - 10)^2 + (y + 16)^2 = 3
\]

So, the equation of the circle is:

\[
(x - 10)^2 + (y + 16)^2 = 3
\]

Would you like more details or have any questions?

Here are some related questions to explore further:

1. How do you derive the equation of a circle from its geometric definition?
2. How can you find the center and radius from the general form of a circle's equation?
3. What transformations can you apply to a circle's equation?
4. How do you determine if two circles intersect, touch, or are disjoint?
5. What is the equation of a circle passing through three given points?
6. How do you find the equation of a tangent line to a circle at a given point?
7. What is the parametric form of a circle's equation?
8. How do you convert the parametric form of a circle's equation to its standard form?

**Tip:** When dealing with equations involving square roots, always ensure to simplify them correctly to avoid errors.

Learn how to find the equation of a circle with center (10, -16) and radius √3. Step-by-step solution provided, including substitution into the standard form equation. Suitable for advanced high school students studying geometry.

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