https://file.aiquickdraw.com/mathbot/file/1726618698291b5ftbrt1.jpg

To find the equation of a circle in standard form, we use the formula:

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

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

From the image:
- The center is \((2, -3)\), meaning \(h = 2\) and \(k = -3\).
- The radius is \(\sqrt{17}\), so \(r = \sqrt{17}\).

Now, substitute these values into the equation:

\[
(x - 2)^2 + (y + 3)^2 = (\sqrt{17})^2
\]

Simplifying:

\[
(x - 2)^2 + (y + 3)^2 = 17
\]

Thus, the equation of the circle is:

\[
(x - 2)^2 + (y + 3)^2 = 17
\]

Would you like further details on how this was derived?

Here are 5 related questions for you:
1. How do you find the equation of a circle when given a diameter instead of the radius?
2. What happens to the equation of a circle if the center is at the origin?
3. Can you convert a circle's equation from general to standard form?
4. How do you determine the center and radius from a general form equation of a circle?
5. What is the geometric interpretation of the equation \((x - h)^2 + (y - k)^2 = r^2\)?

**Tip:** Always square the radius when writing the circle's equation in standard form.

Write the standard form of the equation of the circle with center (2, -3) and radius √17.

Find the standard form of the equation of a circle with center at (2, -3) and radius √17. Learn how to apply the circle equation formula and solve this geometry problem. Suitable for Grades 9-11.

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