Respuesta :
The first step is to find the diameter of the circle. We would do this by applying the formula for finding the distance between two points which is expressed as
[tex]\text{Distance = }\sqrt[]{(x2-x1)^2+(y2-y1)^2}[/tex]From the points given,
x1 = 3, y1 = 0
x2 = 4,y2 = 0
Thus,
[tex]\begin{gathered} \text{Distance = }\sqrt[]{(4-3)^2+(0-0)^2} \\ \text{Distance = }\sqrt[]{1^2\text{ + 0}} \\ \text{Distance = 1} \end{gathered}[/tex]Diameter = 1
Recall,
radius = diameter/2 = 1/2 = 0.5
The standard form of the equation of a circle is expressed as
(x - h)^2 + (y - k)^2 = r^2
h and k are the x and y coordinates of the center of the circle
r is the radius
To find the x and y coordinates of the circle, we would find the midpoint of the diameter. The formula for determining midpoint is expressed as
Midpoint = [(x1 + x2)/2, (y1 + y2)/2
Midpoint = [(3 + 4)/2, (0 + 0)/2)
Midpoint = 7/2, 0
Midpoint = 3.5, 0
Thus,
h = 3.5, k = 0
Substituting these values into the standard equation, we have
(x - 3.5)^2 + (y - 0)^2 = 0.5^2
(x - 3.5)^2 + y^2 = 0.25
