Question

Calculate the center of the circle by completing the square of the equation x2+y2+2x−20y+5=0
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Answer 1

To find the center of the circle, we need to rewrite the given equation in the standard form of a circle equation, which is

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

where (h, k) is the center of the circle and r is the radius.

Given equation:
x^2 + y^2 + 2x - 20y + 5 = 0

Rearranging terms and completing the square for x and y terms separately:

(x^2 + 2x) + (y^2 - 20y) = -5
(x^2 + 2x + 1) - 1 + (y^2 - 20y + 100) - 100 = -5
(x + 1)^2 - 1 + (y - 10)^2 - 100 = -5
(x + 1)^2 + (y - 10)^2 = 96

Now, we see that the center of the circle is at (-1, 10) and the radius of the circle is sqrt(96) = 4√6.