https://r2.erweima.ai/mathbot/image/1725490818416r8uy2jtl.jpg

The problem asks for the standard form of the equation of a circle, given its center and radius. The equation of a circle in standard form is:

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

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

From the image, we are given:
- Center = \((5, 0)\)
- Radius = \(\frac{3}{2}\)

We can now substitute these values into the standard equation:

\[
(x - 5)^2 + (y - 0)^2 = \left(\frac{3}{2}\right)^2
\]

Simplifying the radius squared:

\[
(x - 5)^2 + y^2 = \frac{9}{4}
\]

Thus, the standard form of the equation of the circle is:

\[
(x - 5)^2 + y^2 = \frac{9}{4}
\]

Would you like more details on any part of this explanation?

### Follow-up Questions:
1. What is the general formula for a circle with a different center and radius?
2. How do we convert the standard form of a circle to its general form?
3. What does the equation of a circle represent geometrically?
4. How can you find the diameter of the circle from this equation?
5. What would happen to the equation if the radius were doubled?

### Tip:
Remember that the square of the radius in the standard form must always be positive, which ensures that the equation describes a valid circle.

Find the standard equation of the circle having the given center and radius: Center = (5, 0), Radius = 3/2

Learn how to find the standard form of the equation of a circle with the given center (5, 0) and radius 3/2. This geometry problem covers key concepts and formulas used in the standard equation of a circle. Suitable for students in Grades 9-11.

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