In Exercises 13-20, write the equation of the circle in standard form. Then identify its center

step 1 This is problem number 20 given equation is 9x square plus 9 y square plus 54 x minus 36 y plus

In Exercises 13-20, write the equation of the circle in...

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Key Concepts

Standard Form of a Circle Equation

The standard form of a circle's equation is expressed as (x - h)² + (y - k)² = r², where (h, k) represents the center of the circle and r is its radius. This form is useful because it directly shows the location and size of the circle, making graphing and analysis more straightforward.

Completing the Square

Completing the square is an algebraic method used to transform a quadratic expression into a perfect square trinomial. When applied to the x and y terms in the equation of a circle, this technique helps rewrite the equation in standard form by isolating and restructuring the quadratic parts, thereby making it easier to identify the center and radius.

Identifying Center and Radius

After rewriting the circle's equation in standard form, the coordinates of the center can be directly read as (h, k) and the radius is determined by taking the square root of the constant term on the other side of the equation. This process simplifies the analysis of the geometric properties of the circle.

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