The equation of a circle C is
x^2 +y^2 +2x−4y−44=0 x^2+y^2+2x-4y-44 =0
What is its center (h,k) and its radius r
x^2 + 2 x + y^2 -4 y = 44
x^2 + 2 x + 1 + y^2 - 4 y + 4 = 44+5 = 49
(x+1)^2 + (y-2)^2 = 7^2
center at (-1, 2) radius 7
To find the center and radius of the circle using the given equation, we need to rewrite the equation in the standard form of a circle equation, which is:
(x - h)^2 + (y - k)^2 = r^2
Let's complete the square to transform the given equation into the standard form:
x^2 + 2x + y^2 - 4y - 44 = 0
Rearrange the terms to group the x and y terms together:
(x^2 + 2x) + (y^2 - 4y) - 44 = 0
To complete the square for the x terms, add (2/2)^2 = 1 to both sides of the equation:
(x^2 + 2x + 1) + (y^2 - 4y) - 44 + 1 = 0 + 1
Simplify the x terms and simplify the y terms separately:
(x + 1)^2 + (y^2 - 4y + 4) - 43 = 1
(x + 1)^2 + (y - 2)^2 - 43 = 1
Now, we have the equation in the standard form:
(x - h)^2 + (y - k)^2 = r^2
Comparing the equations, we can see that the center is at the point (-1, 2) and the radius squared is 1 + 43 = 44. Therefore, the radius (r) is the square root of 44, which is approximately 6.63.
So, the center of the circle is (-1, 2) and its radius is approximately 6.63.