Question

(Score for Question 1: ____ of 5 points)

1. The equation of a circle is x2 + y2 - 4x + 2y - 11 = 0. What are the center and the radius of the circle?
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Answer:)

Answer 1

center : (2, -1)

radius : r = 4

Explanation:

Answer 2

The center of the circle:

(2, -1)

The radius of the circle:

r = 4

Explanation:

The first step is to complete the square on both x and y:

x^2 + y^2 -4x + 2y - 11 = 0

x^2 -4x +y^2 +2y = 11

We determine c1 to complete the square on x:

c1 = (b/2)^2

c1 = (-4/2)^2 = 4

We then determine c2 to complete the square on y:

c2 = (2/2)^2 = 1

The equation of the circle is then re-written as:

x^2 -4x + 4 +y^2 +2y + 1 = 11 +4 +1

We then factorize the expressions in x and y separately:

(x-2)^2 + (y +1)^2 = 16

The center of the circle is thus:

(2, -1)

The radius is the square root of 16:

r = 4