Question

What is the equation of this circle in standard form?

Answer 1

The standard equation of a circle of radius r with center at (h,k) is:

(x-h)^2 + (y-k)^2 = r^2.  The two points (2,4) and (9,4) are on this circle.  According to the diagram, the diameter of the circle is 9-2, or 7, which means that the radius is 7/2.    Where is the center?  Starting at M(2,4), and moving 7/2 units to the right will bring us to the center.  So the center is (2+7/2, 4), or
(11/2, 4).  Let's put this data to use:

(x - 11/2)^2 + (y - 4)^2 = (7/2)^2  =  49/4.  This is the simplest form of the equation of this circle.

Answer 2

By using the general equation for a circle, we will see that the equation for this circle is:

(x - 5.5)^2 + (y - 4)^2 = 12.25

How to find the circle's equation?

First, we know that the equation for a circle of radius R centered in the point (a, b) is:

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

In the image, we can see that the circle's diameter extends from the points:

(2, 4) to (9, 4)

So, the y-value does not change, and the change in the x-value (which will give the diameter) is:

9 - 2= 7

So now we know that the diameter is equal to 7 units, and the radius is half of that, so the radius is:

R = 7/2 = 3.5

To get the x-value of the center, we add the radius to the x-value of the smaller point, we get:

2 + 3.5 = 5.5

Then the center of the circle is at the point (5.5, 4)

Now that we know the radius and the center, we can write the equation for the circle:

(x - 5.5)^2 + (y - 4)^2 = 3.5^2

(x - 5.5)^2 + (y - 4)^2 = 12.25

If you want to learn more about circles, you can read:

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