# Graphing Ellipse 4x² + 2y² = 1: Step-by-Step Solution

• José Ricardo
In summary, the conversation is about graphing the ellipse 4x² + 2y² = 1 and the difficulties the person had while trying to find resources for solving this type of equation. They eventually found help on Wikipedia and were able to graph the ellipse by trying different values for x and solving for y.
José Ricardo
Member warned that a reasonable effort must be made

## Homework Statement

Graph the ellipse 4x² + 2y² = 1

4x² + 2y² = 1

## The Attempt at a Solution

2x² + y²/2 = 1/2
I searched for exercises on Google, and i didn't find an equation like that. I watched videoleassons too but it didn't teach this type of equation.

Last edited:
I didn't even think on Wikipedia, thanks @fresh_42!

Try some values of x... what values for y work for your xs?
(You can try to solve for y as a function of x, then plug in choices of x.)

José Ricardo
robphy said:
Try some values of x... what values for y work for your xs?
(You can try to solve for y as a function of x, then plug in choices of x.)
Good! Play values!

Thanks!

## 1. What is the equation of the graph "Ellipse 4x² + 2y² = 1"?

The equation of the graph is 4x² + 2y² = 1.

## 2. How do I graph an ellipse with the equation 4x² + 2y² = 1?

To graph an ellipse with this equation, you will need to follow these steps:

• Step 1: Rearrange the equation to isolate y² on one side: y² = (1-4x²)/2
• Step 2: Find the center of the ellipse by setting 4x² and 2y² equal to 0: (0,0)
• Step 3: Find the x-intercepts by substituting 0 for y and solving for x: (±0.5, 0)
• Step 4: Find the y-intercepts by substituting 0 for x and solving for y: (0, ±0.5)
• Step 5: Plot the center and intercepts on a graph and draw an ellipse connecting these points.

## 3. What is the shape of the graph for the equation 4x² + 2y² = 1?

The graph for this equation is an ellipse.

## 4. How can I determine the major and minor axes of the ellipse graph?

To determine the major and minor axes of an ellipse graph, you can follow these steps:

• Step 1: Rearrange the equation to isolate y² on one side: y² = (1-4x²)/2
• Step 2: Find the larger value between 4x² and 2y² in the equation.
• Step 3: The square root of this value will be the length of the major axis.
• Step 4: The square root of the smaller value between 4x² and 2y² will be the length of the minor axis.

## 5. What is the eccentricity of the ellipse graph with the equation 4x² + 2y² = 1?

The eccentricity of an ellipse can be calculated using the equation e = √(1 - (b²/a²)), where a is the length of the semi-major axis and b is the length of the semi-minor axis. In this case, the eccentricity of the ellipse is e = √(1 - (0.5²/0.25²)) = 0.866.

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