Question

Point A lies on the circle and has an x-coordinate of 1.


Which is the correct calculation of the y-coordinate of point A?

Answer 1

I don't have the circle's equation or the diagram. To find A's y-coordinate you must substitute x = 1 into the circle equation and solve for y.

General method:
- If the circle is (x − h)^2 + (y − k)^2 = r^2, put x = 1:
(1 − h)^2 + (y − k)^2 = r^2
so (y − k)^2 = r^2 − (1 − h)^2
y = k ± sqrt[r^2 − (1 − h)^2] (provided the radicand ≥ 0).

Example: if the circle is x^2 + y^2 = 25, then with x = 1:
y^2 = 25 − 1 = 24, so y = ±√24 = ±2√6.

Give the specific circle equation or diagram and I will compute the numeric y-coordinate(s).