Write the standard equation for the circle. center (10, -6), r = 6.

Solution:

The equation of circle provides an algebraic way to describe a circle, given the center and the length of the radius of a circle.

The equation of a circle is different from the formulas that are used to calculate the area or the circumference of a circle

Given center (10, -6), r = 6.

We know the equation of circle is given as (x - h)² + (y - k)² = r²

Here h = 10 and k = -6 and r = 6

(x - 10)² + (y- (-6))² = 6²

x² - 20x + 100 + y² + 12y + 36 = 36

x² + y² - 20x + 12y + 100= 0

The standard equation of the circle is x² + y² - 20x + 12y + 100 = 0

Write the standard equation for the circle. center (10, -6), r = 6.

Summary:

The standard equation for the circle. center (10, -6), r = 6 is x² + y² - 20x + 12y + 100 = 0.