Final answer:
The equation of the circle with center C at (3/4, -2/3) and radius 3√2 in standard form is (x - 3/4)^2 + (y + 2/3)^2 = 18, which is Option 1.
Step-by-step explanation:
The equation of a circle in standard form is given by (x - h)^2 + (y - k)^2 = r^2, where (h, k) are the coordinates of the center of the circle and r is the radius. In this case, we have a circle with center C at coordinates (3/4, -2/3) and a radius of 3√2. Plugging these values into the standard form equation, we get the equation of the circle as (x - 3/4)^2 + (y + 2/3)^2 = (3√2)^2. Simplifying the radius squared, (3√2)^2 equals 18. Thus, the correct equation of the circle is Option 1: (x - 3/4)^2 + (y + 2/3)^2 = 18.