On a coordinate plane, circle Q is centered at the origin with radius r. Triangle P Q S is shown. Point Q is at (0, 0) and points P is at (x, y). The length of Q P is r, the length of P S is y, and the length of Q S is x. Angle P S Q is a right angle.
Circle Q is centered at the origin with radius r. Point P(x, y) lies on circle Q. Make a conjecture. How can you find an equation relating the radius to the coordinates of point P? Check all that apply.

Notice that ΔPQS forms a right triangle.
Because ΔPQS is a right triangle, apply the Pythagorean theorem.
x² + y² = r²