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I see that you've uploaded an image containing mathematical problems about circles. Let's go through each one step by step and solve them.

1. **Question 1:**
   "Tentukan persamaan lingkaran yang berpusat di titik O (0,0) dengan jari-jari sebagai berikut:"
   
   The problem asks to determine the equation of a circle centered at the origin \((0,0)\) for the following radii:

   a. \( r = 9 \)

   b. \( r = 11 \)

   c. \( r = \sqrt{3} \)

   **Solution:**
   The general equation for a circle centered at \((0,0)\) with radius \(r\) is:

   \[
   x^2 + y^2 = r^2
   \]

   Therefore, for each part:

   a. \( r = 9 \) ⇒ \( x^2 + y^2 = 9^2 = 81 \)

   b. \( r = 11 \) ⇒ \( x^2 + y^2 = 11^2 = 121 \)

   c. \( r = \sqrt{3} \) ⇒ \( x^2 + y^2 = (\sqrt{3})^2 = 3 \)

2. **Question 2:**
   "Tentukan persamaan lingkaran yang berpusat di titik \(P (5, 2)\) dan berjari-jari 8."
   
   **Solution:**
   The general equation for a circle with center \((h, k)\) and radius \(r\) is:

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

   Here, the center is \((5, 2)\) and the radius is \(r = 8\), so the equation becomes:

   \[
   (x - 5)^2 + (y - 2)^2 = 8^2 = 64
   \]

3. **Question 3:**
   "Tentukan persamaan lingkaran yang berpusat di titik \(M (-2, \frac{1}{2})\) dan berjari-jari \(\sqrt{7}\)."
   
   **Solution:**
   Using the same general form of the circle equation, with center \((-2, \frac{1}{2})\) and radius \(r = \sqrt{7}\), the equation is:

   \[
   (x + 2)^2 + \left(y - \frac{1}{2}\right)^2 = (\sqrt{7})^2 = 7
   \]

4. **Question 4:**
   "Tentukan titik pusat dan jari-jari lingkaran berikut:"
   
   The equation is given as:

   \[
   (x + 8)^2 + (y + 11)^2 = 100
   \]

   **Solution:**
   This is already in the standard form of a circle equation \((x - h)^2 + (y - k)^2 = r^2\). Comparing this to the given equation:

   - The center is \((-8, -11)\).
   - The radius \(r\) is \(\sqrt{100} = 10\).

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Let me know if you need more details or explanations!

**Relative Questions:**
1. How do you find the equation of a circle if the center is not at the origin?
2. What changes in the circle equation when the radius is a fraction or irrational number?
3. Can you generalize the equation of a circle in 3D space?
4. How can you find the radius of a circle from its equation?
5. What is the geometric meaning of completing the square in circle equations?

**Tip:** Always remember that the equation of a circle can easily be identified by checking if both the \(x\) and \(y\) terms are squared and have the same coefficients when expanded!

Tentukan persamaan lingkaran dan titik pusat serta jari-jari dari beberapa lingkaran.

This page provides step-by-step solutions to determine the equations of circles with given centers and radii. It covers key concepts such as the general circle equation (x - h)^2 + (y - k)^2 = r^2. Suitable for students in Grades 9-11.

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