Question

Найдите мне радиус круга x^2+y^2-2x+4y=20 srochno

Answer 1

(х^2-2х+1-1)+(у^2+4у+4-4)=20 (х-1)^2+(у+2)^2=20+4+1 (х-1)^2+(у+2)^2=25 R=5 центр OR в точке (1;-2)

Answer 2

Finding the Radius of the Circle

To find the radius of the circle represented by the equation x^2 + y^2 - 2x + 4y = 20, we can rewrite the equation in the standard form of a circle equation, which is (x - h)^2 + (y - k)^2 = r^2. Here, (h, k) represents the center of the circle, and r represents the radius.

Let's complete the square to rewrite the equation in the standard form:

x^2 + y^2 - 2x + 4y = 20

Rearranging the terms:

(x^2 - 2x) + (y^2 + 4y) = 20

To complete the square for the x-terms, we need to add (-2/2)^2 = 1 inside the parentheses. Similarly, for the y-terms, we need to add (4/2)^2 = 4 inside the parentheses:

(x^2 - 2x + 1) + (y^2 + 4y + 4) = 20 + 1 + 4

Simplifying:

(x - 1)^2 + (y + 2)^2 = 25

Comparing this equation with the standard form, we can see that the center of the circle is at (1, -2), and the radius is √25 = 5.

Therefore, the radius of the circle represented by the equation x^2 + y^2 - 2x + 4y = 20 is 5.