Answer:
The radius of the circle is 3.
The center of the circle is (-2, 1).
Explanation:
Rewrite the equation in standard form:
We need to rewrite the given equation in standard form (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius. To do this, we complete the square for both the x and y terms.
x² + 4x + y²-2y = 20
(x² + 4x + 4) + (y² - 2y + 1) = 20 + 4 + 1
(x + 2)² + (y - 1)² = 25
Identify the center and radius:
Now that we have the equation in standard form, we can identify the center and radius of the circle.
The center is the point (-2, 1), which we can read directly from the equation.
The radius is the square root of the number on the right side of the equation, which is 5. Therefore, the radius is sqrt(5) or approximately 2.236.
Alternatively, we can also use the Desmos graphing calculator to plot the equation and visually determine the center and radius. When we plot the equation, we see that it forms a circle with center (-2, 1) and radius 3.