Question

Постройте на координатной плоскости окружность, уравнения которой имеет вид: 1) x²+y²=4 Напиши объяснение как решать и что делать, что откуда по каким правилам/теоремам? Как у доски. Дам наилучшего и поблагодарю и оставлю отзыв.

Answer 1

Никаких теорем и правил, якобы нет... Рисуешь табличку y(x), задаёшь произвольно x, находишь y, получаешь точки зависимости... Потом соединяешь эти точки на координатной плоскости и получаешь окружность.

Answer 2

Plotting a Circle on a Coordinate Plane

To plot the circle with the equation \(x^2 + y^2 = 4\) on a coordinate plane, you can follow these steps:

1. Understand the Equation: - The equation of a circle centered at the origin is given by \(x^2 + y^2 = r^2\), where \(r\) is the radius of the circle. - In this case, the equation \(x^2 + y^2 = 4\) represents a circle centered at the origin with a radius of 2.

2. Plotting the Circle: - To plot the circle, you can start by marking the center of the circle at the origin \((0, 0)\). - Then, you can mark points on the circle by substituting different values of \(x\) and solving for \(y\) using the equation \(x^2 + y^2 = 4\). - For example, when \(x = 2\), \(y\) can be calculated as \(y = \pm \sqrt{4 - x^2}\), giving the points \((2, \sqrt{0})\) and \((2, -\sqrt{0})\).

3. Connecting the Points: - Once you have a few points, you can connect them to sketch the circle.

Using the Equation to Find Points on the Circle

The equation \(x^2 + y^2 = 4\) can be used to find points on the circle by substituting different values of \(x\) and solving for \(y\). For example: - When \(x = 2\), \(y\) can be calculated as \(y = \pm \sqrt{4 - x^2}\), giving the points \((2, \sqrt{0})\) and \((2, -\sqrt{0})\). - When \(x = 0\), \(y\) can be calculated as \(y = \pm \sqrt{4 - x^2}\), giving the points \((0, 2)\) and \((0, -2)\).

Conclusion

By following these steps and using the equation of the circle, you can plot the circle with the given equation on a coordinate plane. If you have any further questions or need additional assistance, feel free to ask!