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The image you uploaded contains a set of mathematical problems involving the identification of the radius of circles from given equations. Let's solve these one by one.

### General Method:
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.

For each equation provided, we will try to rewrite it in a form similar to the standard equation and extract the radius.

### 6) Equation:
\[
x^2 + y^2 + 25x - 22y = 9
\]
First, we complete the square for both \(x\) and \(y\):
- For \(x^2 + 25x\), add and subtract \(\left(\frac{25}{2}\right)^2 = 156.25\).
- For \(y^2 - 22y\), add and subtract \(\left(\frac{22}{2}\right)^2 = 121\).

After completing the square, we can extract the radius \(r\).

### 7) Equation:
\[
-4x + y^2 + 4x - 20y = -9
\]
Simplify this and complete the square for \(y\).

### 8) Equation:
\[
x^2 - 32y = x^2 - 32x + 17
\]
Solve by completing the square.

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I will continue solving these and present the answers for each.

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Identify the radius of each circle given the following equations.

This page helps students learn how to find the radius of circles from various equations by completing the square and rewriting the equation in the standard form of a circle. Suitable for students in Grades 10-12 studying geometry and algebra.

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