Q. 67 - Precalculus Enhanced with Graphing Utilities

Question

Tell whether the given points are on the graph of the equation.

$$\begin{gathered} \mathrm{Equation}: x^2+y^2=4 \\ \mathrm{Points}: (0,2); (-2,2); (\sqrt{2},\sqrt{2}) \end{gathered}$$

Step-by-Step Solution

Answer

The point $\left(0,2\right) \mathrm{and} \left(\sqrt{2},\sqrt{2}\right)$ is on the graph.

Step 1. Given information.

Tell whether the given points are on the graph of the equation.

$$\begin{gathered} \mathrm{Equation}: x^2+y^2=4 \\ \mathrm{Points}: (0,2); (-2,2); (\sqrt{2},\sqrt{2}) \end{gathered}$$

Step 2. Substitute the points in the equation to satisfy the equation.

For the point (0, 2):

$x^2+y^2=4\Rightarrow 0^2+2^2=4\Rightarrow 4=4$

The equation is satisfied, so the point (0,2) is on the graph. 

For the point (-2, 2):

$x^2+y^2=4\Rightarrow {(-2)}^2+2^2=4\Rightarrow 8\ne 4$

The equation is not satisfied, so the point (-2, 2) is not on the graph.

For the point $(\sqrt{2},\sqrt{2})$:
$x^2+y^2=4\Rightarrow {\left(\sqrt{2}\right)}^2+{\left(\sqrt{2}\right)}^2=4\Rightarrow 4=4$

The equation is satisfied, so the point $\left(\sqrt{2},\sqrt{2}\right)$ is on the graph.

Step 3. Conclusion.

The point $\left(0,2\right)$ and $\left(\sqrt{2},\sqrt{2}\right)$ is on the graph.