Question

Graph the circle with center (4, 1) that passes through (4, −4). Find the circumference in terms of π and to the nearest tenth.

Answer 1

The graph of the circle can be seen on the image at the end,and the circumference is 31.4 units.

Explanation:

Remember that the equation of a circle of radius R and center (a, b) is:

(x - a)² + (y - b)² = R²

Here the center is (4, 1), and the radius is the distance between the points (4, 1) and (4, -4)

So the radius is: R = √( (4 - 4)² + (1 + 4)²)R = 5.

Then the circle equation is:(x - 4)² + (y - 1)² = 5²

And the graph can be seen on the image at the end. Remember that the circumference of a circle of radius R is:C = 6.28*R

So, here the circumference is:C = 6.28*5 = 31.4