Q. 68 - Precalculus Enhanced with Graphing Utilities

Question

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

$$\begin{gathered} \mathrm{Equation}: x^2+4y^2=4 \\ \mathrm{Points}: (0,1); (2,0); (2,\frac{1}{2}) \end{gathered}$$

Step-by-Step Solution

Answer

The points $\left(0,1\right); (2,0) \mathrm{and} \left(2,\frac{1}{2}\right)$ is on the graph.

Step 1. Given information.

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

$$\begin{gathered} \mathrm{Equation}: x^2+4y^2=4 \\ \mathrm{Points}: (0,1); (2,0); (2,\frac{1}{2}) \end{gathered}$$

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

For the point (0, 1):

$x^2+4y^2=4\Rightarrow 0^2+4·{\left(1\right)}^2=4\Rightarrow 4=4$

The equation is satisfied, so the point (0, 1) is on the graph. 

For the point (2, 0):

$x^2+4y^2=4\Rightarrow 2^2+4·{\left(0\right)}^2=4\Rightarrow 4=4$

The equation is satisfied, so the point (0,1) is on the graph. 

For the point $\left(2,\frac{1}{2}\right)$:

$x^2+4y^2=4\Rightarrow 2^2+4·{\left(\frac{1}{2}\right)}^2=4\Rightarrow 4+4·\frac{1}{4}=4\Rightarrow 4=4$

The equation is satisfied, so the point $\left(2,\frac{1}{2}\right)$ is on the graph.

Step 3. Conclusion.

The points $\left(0,1\right); \left(2,0\right) \mathrm{and} \left(2,\frac{1}{2}\right)$ is on the graph.