Parabola geometry: chords, focal chords, latus rectum, secant lines | Conic sections | 1

Описание: A parabola is the set of all points in a plane such that, for any point P in the set, the distance to a fixed point, called the focus, is equal to the distance to a fixed line, called the directrix. Like circles, ellipses and hyperbolas, parabolas are conic sections - in other words, curves obtained by slicing a right circular cone with a plane. Specifically, we obtain a parabola when the plane is parallel to exactly one generatrix line of the lateral surface of the cone and intersects its base.

A chord is a line segment whose endpoints lie on the parabola. Focal chords and the latus rectum of the parabola are special types of chords. A parabola can have infinitely many chords.

A focal chord is a chord which passes through the focus. The latus rectum of the parabola is a special type of focal chord. A parabola can have infinitely many focal chords.

The latus rectum of a parabola is a chord that passes through the focus, is parallel to the directrix, and perpendicularly intersects the axis of symmetry. It is a measure of the opening of the parabola, specifically the shorter the latus rectum, the narrower the opening of the parabola; conversely, the longer the latus rectum, the wider the opening of the parabola. The length of the latus rectum is four times the focal length.

Lastly, a secant line is a line that intersects the parabola at exactly two points. Secant lines always cross the parabola, unlike tangent lines, which only touch the parabola at one point. We can draw infinitely many secant lines that intersect a parabola.

----------------------------------------------

I’ve added subtitles to my video. If you struggle to understand the AI voice that narrates the video, you can turn on the subtitles by clicking on the "Subtitles / Closed Captions" icon located in the bottom-right corner of the video player.

----------------------------------------------

Playlists

1) Geometry:    • Geometry  
2) Trigonometry:    • Trigonometry  
3) Arithmetic:    • Arithmetic  
4) Algebra:    • Algebra  
5) Differential calculus:    • Differential calculus  

6) Conic sections:    • Conic sections (geometry)  
7) Triangles:    • Triangles (geometry)  
8) Quadrilaterals:    • Quadrilaterals (geometry)  

----------------------------------------------

Support my work on Patreon so I can keep creating content:   / sohcahtoa1609  .

On my Patreon page, you can also find the Python script that generates the animation.

----------------------------------------------

My social media

Facebook:   / sohcahtoa1609  
Twitter:   / sohcahtoa1609  
Instagram:   / sohcahtoa1609  

----------------------------------------------

Don’t forget to click on the SUBSCRIBE button. Then, click on the bell and select the option "All" from the drop-down list to be the first to know when a new video is released.

Alternatively, you can subscribe to my YouTube channel by clicking on the following link:    / @sohcahtoa1609  .

----------------------------------------------

Lastly, a disclaimer

1) My YouTube videos are intended to serve as guides to understanding mathematics, the English language, linguistics, etc.
2) The voice that narrates my YouTube videos is not mine. It is an AI algorithm that converted my text into speech.
3) The audio tracks used in the background of my YouTube videos are provided by YouTube’s Audio Library.

#conicSections
#conics
#parabolas
#focus
#directrix
#vertex
#axisOfSymmetry
#latusRectum

#Sohcahtoa1609