Question

determine which of the given points are on the graph of the equation. equation: $x^{2}+y^{2}=4$ points: $(0,2)$, $(2, - 2)$, $(sqrt{2},sqrt{2})$ which of these points are on the graph of the equation? select all that apply. a. $(0,2)$ b. $(sqrt{2},sqrt{2})$ c. $(2, - 2)$ d. none of the points are on the graph.

Explanation:

Step1: Test point (0,2)

Substitute $x=0, y=2$ into $x^2+y^2=4$:

$$\begin{align} 0^2 + 2^2 &= 0 + 4 = 4 \end{align}$$

This equals the right-hand side.

Step2: Test point (2,-2)

Substitute $x=2, y=-2$ into $x^2+y^2=4$:

$$\begin{align} 2^2 + (-2)^2 &= 4 + 4 = 8 \end{align}$$

This does not equal 4.

Step3: Test point $(\sqrt{2},\sqrt{2})$

Substitute $x=\sqrt{2}, y=\sqrt{2}$ into $x^2+y^2=4$:

$$\begin{align} (\sqrt{2})^2 + (\sqrt{2})^2 &= 2 + 2 = 4 \end{align}$$

This equals the right-hand side.

Answer:

A. (0,2)
B. $(\sqrt{2},\sqrt{2})$