In Example 2, change the + sign before y² to −.

Data from Example 2

Plot the graph of the equation x² + y² = 25. We first solve this equation for y, and we obtain

which we write as

We now assume values for x and find the corresponding values for y.

If x > 5, values of y are imaginary. We cannot plot these because x and y must both be real. When we show y = ±3 for x = ±4, this is a short way of representing four points. These points are (4, 3),(4, −3),(−4, 3), and (−4, −3).

In Fig. 14.2, the resulting curve is a circle. A circle with its center at the origin results from an equation of the form x² + y² = r², where r is the radius.

y = 25 x, or y = -25 - x, -