Can someone help me simplify this ellipse equation?

Click For Summary
SUMMARY

The discussion focuses on simplifying the ellipse equation 15(x+2)² + (y+3)²/4 = 4. The key steps involve dividing the entire equation by 4 to achieve a standard form where the right side equals 1. This allows for the identification of the parameters a² and b², as well as the center coordinates (h, k). The solution emphasizes that handling the coefficient of 15 can be managed by recognizing that multiplying by 15 is equivalent to dividing by 1/15.

PREREQUISITES
  • Understanding of ellipse equations in the form (x-h)²/a² + (y-k)²/b² = 1
  • Basic algebraic manipulation skills
  • Familiarity with the concept of coefficients in equations
  • Knowledge of how to identify the center of an ellipse
NEXT STEPS
  • Learn about the properties of ellipses and their standard forms
  • Study techniques for manipulating algebraic equations
  • Explore the geometric interpretation of ellipse parameters (h, k, a, b)
  • Practice converting various conic section equations into standard forms
USEFUL FOR

Students studying conic sections, mathematics educators, and anyone looking to improve their algebraic manipulation skills in relation to ellipse equations.

iamsmooth
Messages
103
Reaction score
0

Homework Statement


Graph the following:
15(x+2)^2 + \frac{(y+3)^2}{4} = 4


Homework Equations


\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1


The Attempt at a Solution



I can't seem to get both coefficients to 1, since the right side is only 4. If I multiply the whole thing by 4, I can get rid of the denominator on the y term, but then the coefficient of the x jumps to 60, and 60 won't reduce the coefficient to 1. So I'm stuck. Can anyone help? This is not homework, just a practice question that's bugging me...
 
Physics news on Phys.org
You want to divide both sides by 4 so that you get a 1 on right hand side. Now you only need to collect the denominators into the form a2 and b2 and identify what h and k is. If you have trouble with the 15 then notice that multiplying something with 15 is the same as dividing by 1/15.
 

Similar threads

Replies
4
Views
3K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 2 ·
Replies
2
Views
3K
Replies
3
Views
2K
Replies
8
Views
4K
  • · Replies 11 ·
Replies
11
Views
3K
Replies
3
Views
2K
  • · Replies 10 ·
Replies
10
Views
3K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 16 ·
Replies
16
Views
2K