Finding the focus points of a hyperbola

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SUMMARY

The hyperbola given by the equation x²/4 - y²/4 = -1 can be rewritten in the standard form as y²/4 - x²/4 = 1. To find the focus points of this hyperbola, one must identify the values of 'a' and 'b', where a² = 4 and b² = 4. The foci can then be calculated using the formula c = √(a² + b²), resulting in the foci located at (0, ±√(8)) or (0, ±2√2).

PREREQUISITES
  • Understanding of hyperbola equations and their standard forms
  • Knowledge of conic sections and their properties
  • Familiarity with the distance formula in coordinate geometry
  • Basic algebra skills for manipulating equations
NEXT STEPS
  • Study the properties of hyperbolas, focusing on their foci and directrices
  • Learn about the derivation of the standard form of hyperbolas
  • Explore the relationship between hyperbolas and other conic sections
  • Practice solving problems involving the identification of foci for various hyperbolas
USEFUL FOR

Students studying conic sections, mathematics educators, and anyone looking to deepen their understanding of hyperbolas and their properties.

astrololo
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Homework Statement


So I have the following hyperbola

x^2/4 - y^2/4 = -1

I need to find the focus points of this hyperbola. What is some analytical way to do this ?

Thank yoU!

Homework Equations


I don't know...

The Attempt at a Solution



I need some analytical way to be able to do this. Can somebody give me a hint ?
 
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astrololo said:

Homework Statement


So I have the following hyperbola
$$\frac{x^{'2}}{4}-\frac{y^{'2}}{4}=-1$$
I need to find the focus points of this hyperbola. What is some analytical way to do this ?

Thank yoU!

Homework Equations


I don't know...

The Attempt at a Solution



I need some analytical way to be able to do this. Can somebody give me a hint ?
Use a double $ on this site for LaTeX

$$\frac{x^{'2}}{4}-\frac{y^{'2}}{4}=-1$$
 
SammyS said:
Use a double $ on this site for LaTeX

$$\frac{x^{'2}}{4}-\frac{y^{'2}}{4}=-1$$
Oh thank you for telling me !
 
In future posts, you need to show more of an effort than you did here. If you don't, you will get infraction points.
astrololo said:

Homework Statement


So I have the following hyperbola

x^2/4 - y^2/4 = -1
Or equivalently, ##\frac{y^2}{4} - \frac{x^2}{4} = 1##.
This is a form that is simpler to work with.
astrololo said:
I need to find the focus points of this hyperbola. What is some analytical way to do this ?
See https://en.wikipedia.org/wiki/Hyperbola.
astrololo said:
Thank yoU!

Homework Equations


I don't know...

The Attempt at a Solution



I need some analytical way to be able to do this. Can somebody give me a hint ?
 

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