Sketching Ellipses: Comparing 0 and 8

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

The discussion focuses on sketching the equations of two ellipses represented by the equations 0 = x² - 2x + 4y² and 8 = x² - 2x + 4y². Both equations can be transformed into standard ellipse form by completing the square for the x-terms. The general equation for an ellipse in Cartesian coordinates is derived, demonstrating the importance of completing the square in identifying the shape and properties of the ellipses.

PREREQUISITES
  • Understanding of Cartesian coordinates
  • Knowledge of completing the square in algebra
  • Familiarity with the general equation of an ellipse
  • Basic graphing skills
NEXT STEPS
  • Study the process of completing the square in quadratic equations
  • Learn about the standard form of an ellipse and its properties
  • Explore graphing techniques for conic sections
  • Investigate transformations of conic sections in the Cartesian plane
USEFUL FOR

Students studying algebra, mathematics educators, and anyone interested in graphing conic sections, particularly ellipses.

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 x: x^2 - 2ax = (x - a)^2 - a^2.
 
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?
 
(x- 1)^2+ y^2= x^2- 2x+ 1+ y^2
Do you see how that is connected to x^2+ 2x+ y^2?
 

Similar threads

Equation of hyperbola confocal with ellipse having same principal axes
  • · Replies 4 ·
Replies
4
Views
3K
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