Question

A circle is graphed on this coordinate plane. What is the radius in units of the circle and what is the equation of the circle?​

Answer 1

Answer:

The radius is 4 units, and the equation of the circle is:

(x - 3)^2 + (y + 5)^2 = 16

Step-by-step explanation:

A circle centered at the point (a, b) and with a radius R, is written as:

(x - a)^2 + (y - b)^2 = R^2

In the image, we can see that a segment that cuts the circle in two halves is the segment between the points:

(-1, -5) and (7, - 5)

The distance between these points is the diameter of the circle.

Remember that the distance between two points (x₁, y₁) and (x₂, y₂) is:

D = √( (x₂ - x₁)^2 + (y₂ - y₁)^2)

Then in this case, the distance between the known points is:

D = √( (7 - (-1))^2 + (-5 - (-5))^2)

D = √( 8^2) = 8

The diameter of the circle is 8

Then the radius is:

R = 8/2 = 4

the radius is 4.

Now, to find the center of the circle we just need to go to any of the two extremes of the interval and count 4 units towards the center of the circle, this is:

(-1 + 4, -5) = (3, -5)

or

(7 - 4, -5) = (3, -5)

Then the center of the circle is the point (3, -5) and the radius is R = 4

The equation of the circle is:

(x - 3)^2 + (y - (-5))^2 = 4^2

(x - 3)^2 + (y + 5)^2 = 16