Write the equation of a circle with center (4,5) and a circumference = 16 pi

The required equation in standard form is

Step-by-step explanation:

The equation of a circle with center (h,k) an radius, r units is given by the formula;

The given circle has center (4,5) and the radius can be calculated from the given circumference, which is

We substitute these values into the formula to obtain;

We simplify to get;

Equation of the circle : (x - 4)² + (y - 5)² = 64

Step-by-step explanation:

Equation of the circle

(x - x₁)² + (y - y₁)² = r²

Where (x₁, y₁) be the coordinates of center and r is the radius of circle.

To find the radius

It is given that circumference of circle = 16π

Circumference 2πr = 16

r = 16π/2π= 8

To find the equation of the circle

Center = (4, 5)

(x - x₁)² + (y - y₁)² = r²

(x - 4)² + (y - 5)² = 8²

(x - 4)² + (y - 5)² = 64

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)

32

step-by-step explanation: