a) x 2  y 2  25; x  {0; 1; 2; 3; 4; 5}   zeige graphen

Here is the graph of the equation \( x^2 + y^2 = 25 \) for \( x \in \{0, 1, 2, 3, 4, 5\} \). The blue points represent the positive \( y \)-values, and the red points represent the negative \( y \)-values for each corresponding \( x \)-value.

Would you like more details or have any questions?

Here are some questions you might ask:
1. Can you explain how to derive the positive and negative \( y \)-values from the equation?
2. How would this graph change if the equation were \( x^2 + y^2 = 36 \)?
3. What are the coordinates of the points where \( x \) intersects the circle?
4. Can you plot the graph for \( x \in \{-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5\} \)?
5. What is the radius of the circle in the graph?

**Tip:** When graphing equations involving circles, remember that \( x^2 + y^2 = r^2 \) represents a circle with radius \( r \) centered at the origin.

Explore the graph of the circle x^2 + y^2 = 25 for x values ranging from 0 to 5. This visual representation highlights the relationship between the circle's equation and its graphical representation in the coordinate plane. Learn how the radius affects the circle's dimensions and understand the significance of positive and negative y-values.

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