Writing the equation of a hyperbola given the foci and vertices

Learn how to write the equation of hyperbolas given the characteristics of the hyperbolas. The standard form of the equation of a hyperbola is of the form: (x - h)^2 / a^2 - (y - k)^2 / b^2 = 1 for horizontal hyperbola or (y - k)^2 / a^2 - (x - h)^2 / b^2 = 1 for vertical hyperbola.
The center of the hyperbola is given by (h, k). It is halfway between the two vertices and halfway between the two foci. 'a' is the distance from the center to the vertices and 'b' is the distance from the center to the covertices. 'c' is the distance from the center to the foci. The relationship between a, b and c is a^2 + b^2 = c^2. Using these characteristics of the hyperbola, we can then plug them into the standard equation to obtain the equation of the given hyperbola.
Note that a hyperbola is vertical when it is facing up and down and is horizontal when it is facing right and left. When a hyperbola is vertical, the vertices and the foci are in the y-axis but they are in the x-axis when the hyperbola is horizontal.
#conicsections #hyperbolaconicsections
#conicsections #hyperbolaconicsections
#conicsections #hyperbolaconicsections

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[@brianmclogan]

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you are very welcome Merritt. Keep up the hard work!

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I love it how he puts the answer and how to put the equation right where he puts his other video recommendations so you can’t see the answer.

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Mr. McLogan can you please answer this: Find the standard equation of the hyperbola with vertices (1,9) and (13,9) and one of its foci is (-2,9). Thank you in advance

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You're an absolute math god 🙏 quick question if the hyperbola is vertical does a and b get flipped in the equation

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How would you convert that to Ax^2-By^2=C form

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how did you get -4 to divide them with each other when finding B

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What if you were only given 1 vertex? Would a just end up being 0?

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[@brianmclogan]

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[@mmmountain1968]

you lost me at 2a

[@brianmclogan]

the length of the major axis which is between the vertices is 2a. The distance from each vertex to the center is a

[@LunaStarlight35]

Ha ha! Same

[@klongyss]

Arent the Focis and the Vertices supposed to be flipped on the graph you have here?

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To get the b of the hyperbola you will subtract the a to the both sides??

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Whats the Center, Foci, Vertices, and Asymototes of 9x^2-90x-32y=-305? I'getting confused.

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Where did the 2a come from?

[@brianmclogan]

2a is the length of the major axis

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[@brianmclogan]

Happy to be able to help you out Troy!

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[@oridogie3946]

What if the the givens are only 2 vertices and 1 focus

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[@brianmclogan]

well happy to help you out!

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What if its vertical?

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what math class is this?

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[@brianmclogan]

you are very welcome Parth! happy to be able to help you out!

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[@carlosjoaquinenriquez7192]

How can i find the equation if vertices and covertices are given

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Please answer me sir HAHA!

[@renicelinton9550]

What if you are given the center, one focus and vertex each?

[@brianmclogan]

check the playlist at the end of the video, I have a ton of similar examples

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Which math courses do you teach and which grade level do you teach?

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This year I am teaching Calculus AB and Pre-Calculus. My students range from 10th-12th grade

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i think you forgot to put =1 when you plugged the numbers on the equation. great video though! learned a lot. thanks!

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2021 and still helping kids ☺️

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thank you, I would say just middle of the road

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why did you subtract 9 from 4?

[@brianmclogan]

to solve for c^2, that is the formula for hyperbolas

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Good

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Mr. McLogan seems a nice person, and a committed teacher, and is sloppy in his use of language, and in a rush too often.

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i think you mean but

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6:52 why is h=2 and k=2?

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bc the center is (2,2)

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From Seinfeld?

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[@elijahsharp7414]

i thought the equation was a^2 - b^2 = c^2, but you used regular pythagorean theorem (a^2 + b^2 =c^2

[@brianmclogan]

a^2-b^2=c^2 is for an ellipse, this video is on a hyperbola so the equation I used was correct

[@elijahsharp7414]

ah, thank you, i knew i was mixing something up

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2:26 that should be 7 right?

[@brianmclogan]

no I counted right: 6 units

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Brian McLogan ahh okay thanks sir

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cheers!

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1:02 *WRONNNNG*

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you forgot sir, equals 1 in the equation

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thank you, that is correct

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The girl in the background really got on my nerves, other than that amazing video, really helpful, thank you.

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sorry about that

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ugh yeah the lady in the background is sooo distracting. I really enjoyed your other video on this topic because of less disruptions.

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your a ² and b² are misdeliveries

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sperm cell at 4:54

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Wrong

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What?

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Kind of waste of time watching this 7min video with the girl asking and the teaching making mistakes.

[@loonatheworld5065]

I have a quiz right now, it helped me a lot and now I kinda understand it. Thanks!