Final answer:
The equation of a circle with the center at (12, -8/5) that is tangent to the y-axis is (x - 12)² + (y + 8/5)² = 12².
Step-by-step explanation:
The student's question involves finding the equation of a circle with a given center and the condition that it is tangent to the y-axis. Given the center of the circle is at coordinates (12, -8/5), and since the circle is tangent to the y-axis, the radius of the circle must be 12, which is the distance from the center to the y-axis. To write the equation of the circle in standard form, we use the formula (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius. In this case, the equation of the circle would be (x - 12)² + (y + 8/5)² = 12².