Q. 4 - Precalculus Enhanced with Graphing Utilities

Question

Graph the equation: $x^2+4y^2=4$

Step-by-Step Solution

Answer

The graph of $x^2+4y^2=4$is

Step 1. Given data

The given equation is

$x^2+4y^2=4$

Step 2. Properties of equation

Rearrange the equation into the standard form of the equation of the ellipse

$$\begin{gathered} x^2+4y^2=4 \\ \frac{x^2}{2^2}+\frac{y^2}{1^2}=1 \\ \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 \end{gathered}$$

then

$$\begin{gathered} a=2 \\ b=1 \\ c=\sqrt{a^2+b^2} \\ c=1.73 \end{gathered}$$

vertices are$\left(\pm a,0\right)=\left(\pm 2,0\right)$

foci are$\left(\pm c,0\right)=\left(\pm 1.73,0\right)$

co-vertices are $\left(0,\pm b\right)=\left(0,\pm 1\right)$

Step 3. Graph

Plot a hyperbola of the vertices$\left(\pm 2,0\right)$,co-vertices$\left(0,\pm 1\right)$, and foci $\left(\pm 1,0\right)$to plot the graph of $x^2+4y^2=4$