By applying algebraic procedures, the <em>standard</em> formula of the circle indicates a <em>geometry</em> locus with a center at (x, y) = (-1 , -2) and a radius of 5 units.
<h3>How to identify the radius and the center of a circle</h3>
In this question we have an <em>circle</em> equation in <em>general</em> form and we must transform the expression into <em>standard</em> form to find the center and radius of the <em>geometric</em> locus. An analytical approach consists in completing the square, that is, applying <em>algebraic</em> properties to simplify parts of the <em>circle</em> equation into perfect square trinomials.
Now we proceed to simplify the entire expression:
- x² + 2 · x + y² + 4 · y = 20 Given
- (x² + 2 · x) + (y² + 4 · y) = 20 Associative property
- (x² + 2 · x + 1) + (y² + 4 · y + 4) = 25 Compatibility with addition/Definition of addition
- (x + 1)² + (y + 2)² = 5² Perfect square trinomial/Definition of power/Result
The constants inside the perfect square trinomials correspond with the coordinates of the <em>center</em> and the constant on the right side of the expression contains the radius of the circle.
By applying algebraic procedures, the <em>standard</em> formula of the circle indicates a <em>geometry</em> locus with a center at (x, y) = (-1 , -2) and a radius of 5 units.
To learn more on circles: brainly.com/question/11833983
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