The equation of a circle is given as $(x + 12)^2 + (y - 14)^2 = 50$. We need to find the y-coordinate of the center of the circle.

1. Problem Description

The equation of a circle is given as $(x + 12)^2 + (y - 14)^2 = 50$. We need to find the y-coordinate of the center of the circle.

2. Solution Steps

The general equation of a circle with center $(h, k)$ and radius $r$ is given by:

$(x - h)^2 + (y - k)^2 = r^2$

Comparing the given equation $(x + 12)^2 + (y - 14)^2 = 50$ with the general equation, we can identify the center $(h, k)$ and the radius $r$.

$x + 12 = x - h \implies h = -12$

$y - 14 = y - k \implies k = 14$

$r^2 = 50 \implies r = \sqrt{50}$

The center of the circle is $(-12, 14)$. We are asked to find the y-coordinate of the center of the circle. The y-coordinate is $k$.

3. Final Answer

The y-coordinate of the center of the circle is 14.