Chapter 1.4, Problem 17E

To determine

To graph the ellipse.

Answer to Problem 17E

  

Explanation of Solution

Given information:

Graph the ellipse $4x^2+2y^2=1$ by graphing the functions whose graphs are the upper and lower halves of the ellipse.

Calculation:

Before moving on graphing we have to find the two equations that model the ellipse. Solving for $y$ gives us both:

  $4x^2+2y^2=1$

Now, subtract $4x^2$ from both the sides:

  $2y^2=1-4x^2$

Now, divide both sides by $2$ :

  $y=\frac{1}{2}-2x^2$

Now, take the square root of both sides:

  $y=\pm \sqrt{\frac{1}{2}-2x^2}$

Hence, the two equations are $y=\sqrt{\frac{1}{2}-2x^2}$ and $y=-\sqrt{\frac{1}{2}-2x^2}$ .

Now, we will graph these two function yields:

  

Hence, the result shown in graph.