make a graph representing x^2+y^2=12.25




Here is the graph of the equation \(x^2 + y^2 = 12.25\), which represents a circle centered at the origin with a radius of \( \sqrt{12.25} = 3.5 \).

Let me know if you'd like any further details or have any questions.

Here are five related questions for further exploration:
1. How would the graph change if the equation were \(x^2 + y^2 = 9\)?
2. What is the area of the circle represented by this equation?
3. How would you represent a circle with a different center, such as \((h, k)\)?
4. How would you solve for \(y\) in terms of \(x\) for this equation?
5. What is the length of the circumference of the circle?

**Tip:** To shift the center of the circle, replace \(x^2 + y^2\) with \((x-h)^2 + (y-k)^2\), where \((h, k)\) is the new center.

Explore how to graph the circle equation x^2 + y^2 = 12.25, representing a circle with a radius of 3.5. This solution covers key geometry concepts, including equations of circles, radius calculation, and circle properties. Suitable for students in Grades 9-10.

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