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Graphing a curve with a given equation
Published on November 27, 2024
Geometry
The equation represents an ellipse centered at (-2, 0) with a vertical major axis of length 4 and a horizontal minor axis of length 2.
Question
Answer
Here’s how to solve the problem and graph the curve:
1. Group the x terms:
2. Complete the square for the x terms:
First, factor out the coefficient of
Now, take half of the coefficient of the x term inside the parenthesis (which is 4), square it (which gives 4), and add and subtract it inside the parenthesis:
3. Rewrite the x terms as a perfect square:
4. Simplify and rearrange the equation:
5. Divide both sides by 4 to get the standard form of an ellipse equation:
6. Analyze the equation:
This is the equation of an ellipse centered at
7. Graph the ellipse:
The ellipse is centered at
- Center:
- Vertices:
and - Co-vertices:
and
The graph will be an ellipse elongated vertically, centered at (-2, 0).