Consider the following equation of a circle.

(x−8)2+(y+65)2=259(x−8)2+(y+65)2=259

Step 1 of 3 :  

Find the center, (h,k)(h,k).

The general form of the equation of a circle is:

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

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

Given equation: 

\[
(x - 8)^2 + (y + 65)^2 = 259
\]

Comparing this with the general form, we see that:
- \(h = 8\) (since it's \((x - 8)\)),
- \(k = -65\) (since it's \((y + 65)\), which is equivalent to \((y - (-65))\)).

Thus, the center of the circle \((h, k)\) is:

\[
(h, k) = (8, -65)
\]

Would you like more details or have any questions?

Here are 5 related questions that might help you understand this topic better:
1. How do you find the radius of a circle given its equation?
2. What is the standard form of a circle's equation, and how is it derived?
3. How do changes to the values of \(h\) and \(k\) affect the position of the circle on the coordinate plane?
4. What is the difference between the general and standard forms of the equation of a circle?
5. How can you rewrite the equation of a circle if it's not in the standard form?

**Tip:** Always identify the center and radius of the circle first when given its equation in standard form; this will help you graph and understand its geometric properties more easily.

Consider the following equation of a circle: (x−8)^2+(y+65)^2=259. Step 1 of 3: Find the center (h,k).

Learn how to find the center of a circle given its equation (x−8)^2+(y+65)^2=259. This problem explores geometric concepts related to circles and the center-radius form of a circle's equation. Suitable for students in Grades 9-11.

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