Question

Show me the answer and the work step by step and also please show a graph with coordinates plotted

Answer 1

we have that the graph is

So the answer fo the equation is b. (x-5) + (y-5) = 25.

The diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints are on the circumference of the circle. The given end points of the diameter are (8,9) and (2,1). The center point of the circle is the center of the diameter, which is the midpoint between (8,9) and (2,1) in this case the midpoint is (5,5) because

`((8+2)/(2),(9+1)/(2))=((10)/(2),(10)/(2))=(5,5)`

Find the radius r for the circle. The radius is any line segment from the center of the circle to any point on its circumference. In this case, r is the distance between (2, 1) and (5, 5).

We use the distance formula to determine the distance between the two points that is

`distance=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}`

Substitute the actual values of the points into the distance formula.

`r=\sqrt[]{(5-2)^2+(5-1)^2}=\sqrt[]{3^2+4^2}=\sqrt[]{9+16}=\sqrt[]{25}=5`

Now with the midpoint and the radius we can replace in the equation of the circle with center (h, k) and radius r that is

`(x-h)^2+(y-k)^2=r^2`

Substitute the actual values of the points into the formula we have that the equation of this circle is

`\begin{gathered} (x-5)^2+(y-5)^2=5^2 \\ (x-5)^2+(y-5)^2=25 \end{gathered}`