13 - Conic Sections: Parabola, Focus, Directrix, Vertex & Graphing - Part 1

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Twitter: / jasongibsonmath
In this lesson, you will learn what a parabola is and how it relates to the other conic sections (ellipse, circle, and hyperbola). We will define the parabola in terms of geometry, and use this definition to derive the equation of a parabola. We will then graph the parabola, using the concept of the focus and directrix.
Finally, we will examine and graph vertically oriented parabolas and horizontal parabolas and determine how we know which orientation the parabola has.

[@kaylist1287]

This instructor is so good. Explains things so methodically that makes it easy to follow. I finally understand the significance of Focus and Diredtrix. Thank you , sir. So grateful

[@lamienelondoa3258]

If only all the lecturers were like you, then mathematics will be so easy. So simple with you sir. Thanks a lot.

[@phillipdeck933]

You are the best. I just watched about 3 other videos on parabolas with a different instructor l got lost then l watched this one, you made it very clear l got it now and l will make sure it's you on my future lessons. Thank you.

[@abdulmousa3955]

Brilliant instructor. I wish I have an instructor like him when I was in high school 30 years before.

[@MathAndScience]

Good luck in your studies! Jason, MathAndScience.com

[@qzorn4440]

@@MathAndScience this will help in making a radio telescope. thanks. 🌟

[@MathAndScience]

@@qzorn4440 that’s awesome

[@user-xv9dv4go2d]

Great job! I see the equation of parabola hard but from your details explanation l get it know, thanks alot

[@elicubillo313]

Great teacher! Not everyone goes into detail like you do...

[@sudiptoits]

Superb, most excellent explanation Wow👍👍 I tried to search directrix and vertex of conic sections on internet but I couldn't understand half of it but when I watched your vids my tired and defeated brain sprung up into action and in a sec I understood all there is

[@dongstv4574]

PROTECT THIS MAN AT ALL COST

[@kagamer21]

Hey man, thank you. I really like your teaching style All the best

[@MathAndScience]

Wow thanks!

[@yrrejogoc]

This is a good teacher ver detailed when it comes to explain in conic section...i love the way he teach...he did not use any shortcut to fast the lesson.....he helps me a lot....because i am bad at mathematics equation especially like this.😅

[@felixyongco4420]

Now it is very clear why the parabola opens downward . After many , many long years of researching.. Sir thank you so much.And the Focus vs. the Directrix on equal measured distance..

[@yumyumpowakatyra9725]

Wow… I understand COMPLETELY. You’re very good!

[@ect2012cool]

Great explanation for solving the problems.

[@kabouch]

I would think of a parabola opening rightward (x=ay^2+by+c) as an invertible form of one opening upward(y=ax^2+bx+c). The same her for the leftward and downward parabolas are also inverse. Knowing that conic curves are not functions but quadratic relations.

[@indirapoudel3409]

Sir can we make more than one parabolas (all opening in one direction) from a single vertex?

[@user-ms9xd3pt5l]

Best teacher 🎉🎉😊

[@pastorbrightamegazo9231]

Great job! I now understand this

[@T2Exile]

love this lesson

[@bymoviestube9202]

The DEATH STAR!!! Always knew your knowledge wasn't from this Galaxy.

[@cowboyteacher5243]

Wow teaching like a pro. Thanks

[@MathAndScience]

Thank you so very much!!

[@mumtazhamid]

Wonderful : )

[@couchsurfer2856]

Most execellent explaination

[@MathAndScience]

Thank you so much!

[@kabouch]

Would you please illustrate this: what is the link between a satellite dish which is a 3-D shape and the parabolic curve which is planar? In other words, do all the sectioned parabolic curves of the satellite dish share the same focus?

[@MathAndScience]

Yes exactly. There is a single focus of the dish in the center and above the bottom. If you slice the dish down the center then the focus looks like it does in the diagrams I draw. Basically if you form a solid by taking a parabola as we have drawn in the board and revolving it about the vertical axis, you get the traditional dish shape we use for satellites. This is why you see the receiver hovering over the dish. It is at the focus.

[@electric_sand]

Smart question

[@tresajessygeorge210]

THANK YOU... SIR...!!!

[@musashi4856]

Superb tutorial! Question: how can one determine the focus or directrix of a parabola if neither are provided? For example, y=x^2 is all that is given.

[@carultch]

Rearrange the equation so it matches the following form, once you identify that it is a vertical axis parabola: 4*p*(y − k) = (x−h)^2 Given the equation y=x^2, you can see by inspection that both h and k are zero. In order for the coefficient on y to equal 1, since it equals 1 on both sides of y=x^2, this means p has to equal 1/4. Once you have h, k, and p, the equation for the directrix will be y=k-p, and the focus will be at (h, k+p). In our case, that means y=-1/4 is the equation of the directrix, and (0, +1/4) is the location of the focus.

[@jaaallhaque7941]

hi sir, I like your style of explanation.🇧🇩🇧🇩

[@hemarajue2736]

We know that circle is not a function as it fails a vertical line test. Similarly the ellipse and hyperbola. The parabola passes vertical line test when it opens up or down but fails at when opens sideways. Does it mean that all conic sections are not functions?

[@carultch]

No, because you just provided a counterexample. One counterexample disproves an "all" statement, and in this case, it is the family of parabolas opening vertically that disproves the statement "all conic sections are non-functions".

[@hemarajue2736]

@@carultch yes,we have to consider the different cases for each conic section.

[@muntoo1]

Is not all points on an horizontal line through the the vertex, equidistant from focus and directrix?

[@jasongrinibraanen2691]

If you mean two parallell lines. Well, all points on the one line will be in equal distance to the other line. But remember what condition we need to satisfy. That any point on the curve, will be in same distance to both the point(focus) and the line(directrix). Let my try to prove that a parallell line to the directrix does not satisfy the parabola conditions: So we have a line. a parallell directrix, and a focus. Line to focus: Two points on the line may have different distances, a and b to the focus. Line to directrix: because the line and the directrix are parallell, two points on the line will always have the same distance, c, to the directrix. This means we need that a=c and b=c. But since a ≠ b, then both a and b can't be equal to c. This means the distances can't be equal for all givens points on the line. Qed Anyway, I think this is interesting. And similar question crossed my mind. Are there any other shapes that also satisfy the parabola conditions? And for me it seems logic that this will be the only solution in a 2d-plane.

[@qzorn4440]

this is wonderful information to relearn the parabola in making a SDR 1420 MHz radio telescope dish to monitor the deep space hydrogen line. WOW that's a mouth full. 😎 Thanks a lot. What about pointing the parabola at angles 45 degrees or 60 degrees, etc. as in tracking the movement of a star?

[@MathAndScience]

Welcome!

[@ananthpadmanaban650]

At 54.44 instead of x-k=a(y-k) it should be x-h =a(y -k) . I am highlighting it as one could easily get misguided and confused due to this small error .

[@MathAndScience]

Thank you!

[@hilllanza]

Nice.👍👍👍

[@MathAndScience]

Thank you so much! Jason, MathAndScience.com

[@kabouch]

To prove P=1/4a, just consider the vertex at (h,0) and the focus is at (h,p), and go on the proof the same way to end up with the following equation y=(x-h)^2/4p

[@electric_sand]

You mean "to prove a=1/4c"?

[@alltosee7070]

time goes so fast when you teach

[@MathAndScience]

I love to hear this. Thank you!

[@501promo]

For just a second when I read the title, I thought this vid was reviewing new ED meds in minute detail...

[@501promo]

For the simple folk: 1) Parabona or Paraballa 2) Foc_us 3) Dir(ty)_irect(ion)_trix 4) Vert(icle)_ex(tender)

[@andrewkiongo5548]

I think it should be a=4c

[@abbasbookwala]

Yes..I think so

[@abbasbookwala]

I just derived it..a=1/4c is correct

[@wisdomnwannah4332]

What is the name of this teacher?

[@MathAndScience]

Hi, my name is Jason Gibson. Thanks!

[@wisdomnwannah4332]

@@MathAndScienceI am really in love with your teaching and I'll be willing to have you as my mentor in electrical engineering. Do you have a platform where I can get all your videos on electrical engineering? There are some lecturers that I find it difficult to understand but your case is different

[@MathAndScience]

charlie dave hi yes you can get everything at www.MathAndScience.com. Good luck in your studies!

[@bidarvandi]

watch this 2 or3 times

[@user-lr6zf1nv4z]

I've it

[@DarthVader-gp4kr]

Don't care much about the drawings. We get the picture