Design a circular waveguide field with a lossless non-magnetic dielectric medium. The waveguide must operate in a single mode over a bandwidth of 1.5 GHz. The radius of the guide is 1.12 cm. (a) Find the relative permitivity of the medium that filled the waveguide.
(b) Find the lower and upper frequencies of the operation.

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.