Final answer:
To calculate the y-coordinate of point A on a circle with x = 1, we need the circle's radius to use the formula x² + y² = r². The provided choices do not include necessary information such as the radius to calculate y.
Step-by-step explanation:
To find the y-coordinate of point A that lies on a circle with an x-coordinate of 1, we can use the formula for a circle centered at the origin (0,0), which is x² + y² = r², where r is the radius of the circle. Assuming we know the radius, we substitute x = 1 into the formula to find y. This is not one of the choices presented in the question, indicating that the problem might be missing some information or another part of the calculation is needed.
However, let's examine one of the options that seems closely related to this concept: option (b). (0 - 1)² + (0 - y)² = r². This resembles a form of the Pythagorean theorem applied to a circle's equation but doesn't help us without the value of the radius. Without the value of r, we cannot perform the calculation.
If the radius was given, for example as r = √2, then we could calculate y by rearranging the equation as follows: 1 + y² = 2, which simplifies to y² = 1, and y could then be ±√1. Hence y would be ± 1.