Introductions to conics and circle

# Introductions to conics and circle
## Analytic Geometry
### Arturo Sánchez González
### <a href="mailto:arturo.sanchez@upaep.mx" class="email">arturo.sanchez@upaep.mx</a>
### August 2021

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# Motivation: CONIC SECTIONS

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# Why are they called conic sections?

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class: clear, center, middle

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# First approach

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# How do we define a circle? (1/2)

<span style="font-size:30px">A <span style="color:green">**CIRCLE**</span> is

<span style="font-size:33px">_**the set of all points in the plane** that are <span style="color:blue">a fixed distance</span> (the <span style="color:blue">radius</span>) from <span style="color:red">a fixed point</span> (the <span style="color:red">center</span>)_
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<img src="circle.png" width="110%" style="display: block; margin: auto;" />
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# How do we define a circle ? (2/2)

</br>
- <span style="font-size:27px"> the radius `\(\color{red}{r}\)`: <span style="color:blue"> it is a number</span>
  
  * <span style="font-size:25px"> Can it be negative?
  
  * <span style="font-size:25px"> What happen if `\(r=0\)`?

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- <span style="font-size:27px"> the center `\(\color{red}{C(h,k)}\)`: <span style="color:blue">it is a point in the plane
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<img src="circle.png" width="110%" style="display: block; margin: auto;" />
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