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

To find the y-coordinate of point A on a circle where you know the x-coordinate, you need to know the equation of the circle. The standard equation of a circle with center \((h, k)\) and radius \(r\) is:

\[
(x - h)^2 + (y - k)^2 = r^2
\]

If you have the specific values for \(h\), \(k\), and \(r\), you can substitute the x-coordinate (in this case, \(x = 1\)) into the equation to solve for \(y\).

For example, let's say the circle has a center at \((h, k) = (0, 0)\) and a radius \(r = 5\). The equation would be:

\[
(x - 0)^2 + (y - 0)^2 = 5^2
\]

Substituting \(x = 1\):

\[
(1 - 0)^2 + (y - 0)^2 = 25
\]
\[
1 + y^2 = 25
\]
\[
y^2 = 24
\]
\[
y = \pm \sqrt{24} = \pm 2\sqrt{6}
\]

So in this example, the y-coordinates of point A could be \(2\sqrt{6}\) or \(-2\sqrt{6}\).

If you provide the center and radius of the circle, I can help you find the specific y-coordinate of point A.