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The question asks to find the equation of a circle with center at \((1, -2)\) and radius \(3\).

The standard equation of a circle is given by:

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

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

In this case, the center is \((1, -2)\) and the radius is \(3\).

Substitute these values into the equation:

\[
(x - 1)^2 + (y + 2)^2 = 3^2
\]

\[
(x - 1)^2 + (y + 2)^2 = 9
\]

Thus, the equation of the circle is:

\[
(x - 1)^2 + (y + 2)^2 = 9
\]

Would you like further details or have any questions?

### Related Questions:
1. How do you derive the equation of a circle from the general form to standard form?
2. What happens if the radius is zero? What kind of geometric figure does this represent?
3. How do you find the radius of a circle given the equation in standard form?
4. What is the equation of a circle if the center is at the origin?
5. How do you transform the equation of a circle if it is shifted along the x- or y-axis?

### Tip:
Always double-check whether the center and radius are correctly substituted into the standard equation of the circle to avoid errors.

Find the equation of the circle whose center is (1, -2) and radius is 3.

Learn how to find the equation of a circle with center at (1, -2) and a radius of 3 using the standard formula for circle equations. Suitable for students in Grades 8-10.

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