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

step 1 We have problem number 18 given equation is x squared plus y square minus 10 x minus 6y plus 25

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

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Key Concepts

Completing the Square

Completing the square is a method used to convert a quadratic expression into a perfect square trinomial. This technique is essential for rewriting the general equation of a circle into its standard form by rearranging and grouping the x and y terms separately, thereby revealing the center and radius of the circle when compared to the standard equation.

Center and Radius

The center and radius are the fundamental geometric characteristics of a circle. Once the equation of the circle is written in standard form, the coordinates of the center are directly given by (h, k) and the radius is the square root of the constant on the right-hand side of the equation, ensuring that any circle can be uniquely defined by these parameters.

Standard Form of a Circle

The standard form of a circle's equation is given by (x - h)² + (y - k)² = r², where (h, k) represents the center of the circle and r is its radius. This form makes it straightforward to identify the geometric properties of the circle from the equation.

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