The word "intercept" means crossing point, and the yintercept of a graph refers to the point at which the equation crosses the yaxis of the coordinate plane. When a point is on the yaxis, it is neither to the left nor the right of the origin. Therefore, it is located at the spot in the equation where x equals zero. Because a circle is round, it can cross the yaxis twice and have up to two yintercepts. However, you find the yintercept(s) of a circle the same way you would for any other equation  by substituting "0" for x.

Substitute "0" in for x in the standard form of the equation of a circle  (xh)^2 + (yk)^2 = r^2, where h and k are integers and r stands for the radius of the circle. For example, (x3)^2 + (y+4)^2 = 25 becomes (03)^2 + (y+4)^2 = 25 when plugging "0" in for x.

Square the part of the equation that used to have the x, the h value. Then, subtract that from both sides. Here, you will get 9 + (y+4)^2 = 25, then (y+4)^2 = 16.

Take the positive and negative square root of both sides to create two linear equations. For instance, in the example above, you will have y + 4 = 4 and y + 4 = 4.

Solve each equation for y to get your yintercepts. In this case, you subtract 4 from both sides in both equations to end up with (0, 8) and (0, 0).
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