Question

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

Answer 1

Answer:

x2=y2=r2

Step-by-step explanation:

edge

Answer 2

Answer:

The relation $x^{2} +y^{2} =r^{2}$ is explained below.

Step-by-step explanation:

P(x, y) is a point on the circle. Q is the origin. Join PQ.

PQ is the radius.

Therefore, PQ = r

Draw PS perpendicular to the x-axis.

Now, ΔPQS is a right triangle.

By Pythagoros theorem,

$PQ^{2}=PS^{2} +QS^{2}$

$r^{2}=x^{2} +y^{2}$

$x^{2} +y^{2} =r^{2}$