Question

The diameter of Circle Q terminates on the circumference of the circle at (3,0) and (4,0) Writein standard form Show all of your work for full credit

Answer 1

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

`\text{Distance = }\sqrt[]{(x2-x1)^2+(y2-y1)^2}`

From the points given,

x1 = 3, y1 = 0

x2 = 4,y2 = 0

Thus,

`\begin{gathered} \text{Distance = }\sqrt[]{(4-3)^2+(0-0)^2} \\ \text{Distance = }\sqrt[]{1^2\text{ + 0}} \\ \text{Distance = 1} \end{gathered}`

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