Question

Complete the square to rewrite the following equation. identify the center and radius of

Answer 1

By applying algebraic procedures, the standard formula of the circle indicates a geometry locus with a center at (x, y) = (-1 , -2) and a radius of 5 units.

How to identify the radius and the center of a circle

In this question we have an circle equation in general form and we must transform the expression into standard form to find the center and radius of the geometric locus. An analytical approach consists in completing the square, that is, applying algebraic properties to simplify parts of the circle equation into perfect square trinomials.

Now we proceed to simplify the entire expression:

1. x² + 2 · x + y² + 4 · y = 20     Given
2. (x² + 2 · x) + (y² + 4 · y) = 20     Associative property
3. (x² + 2 · x + 1) + (y² + 4 · y + 4) = 25     Compatibility with addition/Definition of addition
4. (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 center and the constant on the right side of the expression contains the radius of the circle.

By applying algebraic procedures, the standard formula of the circle indicates a geometry 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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