Sketching Ellipses: Comparing 0 and 8

  • Context: Undergrad 
  • Thread starter Thread starter JC3187
  • Start date Start date
  • Tags Tags
    ellipses
Click For Summary

Discussion Overview

The discussion revolves around sketching the equations of two curves, specifically 0 = x² - 2x + 4y² and 8 = x² - 2x + 4y². Participants are exploring how to determine if these equations represent ellipses and the methods for sketching them.

Discussion Character

  • Exploratory
  • Mathematical reasoning

Main Points Raised

  • Some participants inquire about the best methods for sketching the given equations and how to confirm they are both ellipses.
  • One participant suggests completing the square in x as a potential approach to analyze the equations.
  • Another participant asks for clarification on the general equation for an ellipse in Cartesian coordinates and the relevance of completing the square.
  • A participant presents a transformation of the equation, showing how (x - 1)² + y² relates to the original equation.

Areas of Agreement / Disagreement

Participants are generally exploring the same problem but have not reached a consensus on the methods or the implications of their findings regarding the equations.

Contextual Notes

There are unresolved steps in the mathematical reasoning, particularly regarding the completion of the square and its application to the equations in question.

JC3187
Messages
15
Reaction score
0
Hi guys,

What is the best way to sketch

0 = x2 - 2x + 4y2 And
8 = x2 - 2x + 4y2

?

How do I sketch these two and how do I know they're both ellipses?
Thank you.
 
Physics news on Phys.org
JC3187 said:
Hi guys,

What is the best way to sketch

0 = x2 - 2x + 4y2 And
8 = x2 - 2x + 4y2

?

How do I sketch these two and how do I know they're both ellipses?
Thank you.

Complete the square in [itex]x[/itex]: [itex]x^2 - 2ax = (x - a)^2 - a^2[/itex].
 
Then what do i do?
 
JC3187 said:
Then what do i do?
What is the general equation for an ellipse in Cartesian coordinates? Can you see why completing the square helps?
 
[tex](x- 1)^2+ y^2= x^2- 2x+ 1+ y^2[/tex]
Do you see how that is connected to [tex]x^2+ 2x+ y^2[/tex]?
 

Similar threads

Equation of hyperbola confocal with ellipse having same principal axes
  • · Replies 4 ·
Replies
4
Views
4K
High School How can I accurately sketch a complex graph with functions like 2x-⅜+¾e^-2x?
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Equation or semi-axes of the ellipse
  • · Replies 6 ·
Replies
6
Views
4K
Undergrad Eccentric anomaly of ellipse-circle intersections
  • · Replies 4 ·
Replies
4
Views
2K
MHB Bruno's question at Yahoo Answers (Tangent line to an ellipse).
  • · Replies 2 ·
Replies
2
Views
2K
MHB Intersection of line with ellipse - given difference of eccentric angles
  • · Replies 6 ·
Replies
6
Views
6K
Graduate Calculate double integral of the intersection of the ellipse and circle
  • · Replies 5 ·
Replies
5
Views
5K
Undergrad How Can Nested Summation Functions Be Simplified or Reversed?
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad The tangent to an ellipse from polar coordinates
  • · Replies 1 ·
Replies
1
Views
5K
MHB Sketching graphs with extreme values with the Given Information
  • · Replies 6 ·
Replies
6
Views
2K