To begin, let us determine the point of intersection of these two lines by setting the equations equal to each other:

To find the y-coordinate, substitute into one of the equations. Let's use :

The center of our circle is therefore .

Now, recall that the general form for a circle with center at  is

For our data, this means that our equation is:

Recall that the equation of a circle is defined as:

Where  is the center of the circle.

Given the data we have, we know that the radius of the circle must be  (half the diameter).  Thus, we know that the equation of the circle in question must be:

Recall that the equation of a circle is defined as:

Where  is the center of the circle.

So, you must first find the center of the circle in question.  This you can do by finding the midpoint of the two points given to us.  Since they represent a diameter of the circle, their midpoint must be the center of the circle.

Recall that the midpoint of two points is found by the equation:

Thus, for our points, we have:

This is:

 or 

Now, the distance between our two points is very easy, as it lies on a horizontal line.  Thus, it is just:

If this is the diameter, the radius of the circle is .  Thus, we know based on our data that our circle's equation must be:

To begin, recall that the equation of a circle is defined as:

, where  is your center point.

Now, for this question it is a bit trickier, for our center point is not a pair of numbers but instead is a set of variables (or at least constants that are not specific numbers). So, for this information, you would know:

None of your answers are in this format (except two that are obviously wrong because of the signs). You need to foil out your groups to find the right answer:

Carefully done, this is:

The formula for a circle centered around a point  with radius  is given by:

.

Thus we see the answer is 

The general formula for a circle centered about points  with a radius of  is:

.

Since we are centered about the origin both  and  are zero. Thus the equation we have is:

 after simplifying 

The basic formula for a circle in the coordinate plane is , where  is the center of the circle with radius .

Using this, we can simply substitute  for ,   for , and  for . Customarily,  is simplified for the final equation.

 ----> .

The basic formula for a circle in the coordinate plane is , where  is the center of the circle with radius .

Since  refers to the y-coordinate of the center, and we know that any point on the x-axis has a y-coordinate of , we merely need to look for the equation in which k does not exist.

Note that despite meeting this requirement,  still does not qualify, as it is not an equation for a circle at all. Without including a value for , this equation describes a parabola.

The basic formula for a circle in the coordinate plane is , where  is the center of the circle with radius .

We know that , since that is the only way a diameter can pass through the circle and intercept an x-coordinate of  at both ends. , on the other hand, may be seen as halfway between one y-coordinate and the other y-coordinate. Averaging the two, we get:

, so  becomes our . Since the diameter is  units long, we know the radius is half that, so .

Thus, we have .

The formula for a circle is 

 is the coordinate of the center of the circle, therefore  and .

The area of a circle:  

Therefore: