Q. 65 - Precalculus Enhanced with Graphing Utilities

Question

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

$$\begin{gathered} \mathrm{Equation}: {\mathrm{y}}^2={\mathrm{x}}^2+9 \\ \mathrm{Points}: (0,3); (3,0); (-3,0) \end{gathered}$$

Step-by-Step Solution

Answer

The point (0,3) on the graph of the equation.

Step 1. Given information.

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

$$\begin{gathered} \mathrm{Equation}: {\mathrm{y}}^2={\mathrm{x}}^2+9 \\ \mathrm{Points}: (0,3); (3,0); (-3,0) \end{gathered}$$

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

For the point (0, 3):

$y^2=x^2+9\Rightarrow 3^2=0^2+9\Rightarrow 9=9$

The equation is satisfied, so the point (0,3) is on the graph. 

For the point (3, 0):

$y^2=x^2+9\Rightarrow 0^2=3^2+9\Rightarrow 0\ne 18$

The equation is not satisfied, so the point (3,0) is not on the graph. 

For the point (-3, 0):

$y^2=x^2+9\Rightarrow 0^2={(-3)}^2+9\Rightarrow 0\ne 18$

The equation is not satisfied, so the point (-3, 0) is not on the graph.

Step 3. Conclusion.

The point (0,3) is on the graph.