Question

Determine the radius of the circle. ​

Answer 1

Ответ:

Пошаговое объяснение:

Разделим уравнение на 4:

x² + y² + 5x - 4y + 6,25 = 0

Выделим полные квадраты:

x² + 5x = x² + 2·x·2,5 + 2,5² - 2,5² = (x + 2,5)² - 6,25

y² - 4y = y² + 2·y·2 + 4² - 4² = (y + 2)² - 16

Получем:

(x + 2,5)² - 6,25 +  (y + 2)² - 16  + 6,25 = 0

(x + 2,5)² +  (y + 2)² =  4²

Радиус окружности:

R = 4

Answer 2

To determine the radius of a circle, we need to know some information about the circle. The radius is defined as the distance from the center of the circle to any point on its circumference. There are several ways to find the radius depending on the information given.

If the Diameter is Known:

If you know the diameter of the circle, which is the distance across the circle passing through the center, you can find the radius by dividing the diameter by 2. The formula for finding the radius from the diameter is:

radius = diameter / 2

For example, if the diameter of the circle is 10 units, then the radius would be 10 / 2 = 5 units.

If the Circumference is Known:

If you know the circumference of the circle, which is the distance around the circle, you can find the radius using the formula:

radius = circumference / (2 * π)

Here, π (pi) is a mathematical constant approximately equal to 3.14159. So, if the circumference of the circle is 20 units, the radius would be 20 / (2 * 3.14159) ≈ 3.1831 units.

If the Area is Known:

If you know the area of the circle, you can find the radius using the formula:

radius = √(area / π)

Here, √ represents the square root function. For example, if the area of the circle is 25 square units, the radius would be √(25 / 3.14159) ≈ 2.82 units.

If the Coordinates of Three Points on the Circle are Known:

If you have the coordinates of three points on the circle, you can determine the radius by using the equation of a circle. The equation of a circle in the coordinate plane is:

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

where (h, k) represents the coordinates of the center of the circle and r represents the radius. By substituting the coordinates of any of the three points and solving for r, you can determine the radius of the circle.

These are some of the common methods to determine the radius of a circle based on the information provided. Choose the method that suits your available information, and you will be able to find the radius of the circle.