Question

I am going to attach a picture of the question as you can see it's already been answered well my teacher wants me to show how she got that answer.

Answer 1

C

1) Since the diameter of a circle is at (3,-7) and (5,7) then we can find the radius this way.

(x-h) +(y-k)² = r²

2) The Center is at the midpoint of the Diameter, then let's find out the midpoint of the line whose endpoints are (3,-7) and (5,7)

`\begin{gathered} M=((x_1+x_2)/(2),\text{ }(y_1+y_2)/(2)) \\ M=((3+5)/(2),(7-7)/(2)) \\ M=(4,0) \end{gathered}`

2.2) Now, we need to find out the radius. Let's pick one of those points (5,7) and the Midpoint (4,0) and find out the distance:

`\begin{gathered} d=\sqrt[]{(x_1-x_2)^2+(y_1-y_2)^2}_{} \\ d=\sqrt[]{(5-4)^2+(7-0)^2} \\ d=\sqrt[]{50} \end{gathered}`

This distance between one of those endpoints and this midpoint is the radius.

3) Finally, let's plug into the equation of the Circle the following:

`\begin{gathered} (x-4)^2+y^2=(\sqrt[]{50})^2 \\ (x-4)^2+y^2=50 \end{gathered}`

Hence, the answer is C