FInding Circle Diameter

Question

A circle in the xy-plane has a diameter with endpoints (-1,-3) and (7,3). If the point (0,b) lies on the circle and b>0, what is the value of b?

Answer 1

The center of the circle is the midpoint of the diameter. Use the midpoint formula.

The radius of the circle is 1/2 the diameter. Use the distance formula to find the length of the diameter, then take half to find the radius.

Now use the center-radius form for the equation of a circle with center at (h,k) and radius r to get the equation.

Finally substitute 0 for x in that equation, solve for y, and that will be the value of b.

After performing the above steps you can check your work here:

desmos.com/calculator/johbnfnwcb