Finding the equation of an ellipse given a point and vertices

Learn how to write the equation of an ellipse from its properties. The equation of an ellipse comprises of three major properties of the ellipse: the major radius (a), the minor radius (b) and the center (h, k). The ellipse is vertical if the major radius in vertical and the ellipse is horizontal if the major radius is horizontal.

The center of an ellipse is halfway between the major/minor axis or the foci. When given the vertices or the co-vertices of an ellipse, the major radius of an ellipse is the distance between the center of the ellipse and its vertices while the minor radius of an ellipse is the distance between the center of the ellipse and its co-vertices. We can plug in the coordinate of the point we were given for x and y in the equation of an ellipse to obtain the remaining properties.

After obtaining the center, the major and the minor radius, they are plugged into the equation of an ellipse to obtain the desired equation.

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[erikacolbert]

okay but we need one with the foci and a given point

[Alex-glhm]

Best teacher I’ve ever come across on YouTube

[angkimochi-cf]

This guy is the reason why we need youtube

[BackHawk]

Thanks. This really opened my eyes! You should demonstrate on how to find the standard equation when given only two passing points...

[richypadin]

Excellent explanation of the topic! I'm a Civil Engineer, this and other of your videos help me out to clarify some doubts for the FE Exam for Engineers!! From Puerto Rico a big Two Thumbs Up for you!

[lenardmangalus]

What if there's no given value of vertex?
What if the only given is a foci and a point

[ojuskhanolkar]

Dear Mr. Mc.Logan,

Thank you so much for such a great tool! I was a little confused on your beginning though: how could you so clearly state that the ellipse was going to be vertical? I couldn't tell if the vertices were given for the major axis or the minor axis.
Thank you again!

[miselle]

Finally I'll learn from here😀 thank you!!

[toomanycactus]

my precal professor mentioned you on the first day of class but couldn’t remember your name so I said it’s Brian Mclong 😂 I was pretty close tho.

[yuewang]

your videos are super super helpful but god that girl in the background is annoying

[Mixedmetalhead]

Thanks Mr. McLogan! My textbook had me really stuck and your video made it super clear.

[soyyy]

What if b=0? Wouldn't that make it incorrect? I remember that my teacher taught me an alternative way than cross multiplying but I can't remember what exactly it might mistaken :p

[coralaisly]

lol thanks! I was looking for help on this topic and stumbled across you solving the exact problem I got stuck on from my homework! Thanks much!

[Afroguy]

so i take college algebra and i was a bit confused on a particular problem so i figured ill just look up a tutorial on how to find equation given the vertex and one point, turns out the EXACT SAME problem you did this tutorial on happened to be the one i needed help on, as in my textbook it say v(0, plus/minus5) and (4, 2)

[captainostrichpants]

This helped me a lot. Great video, very clear

[carlocapil]

Got curious which standard form will I'll be using.

[orochich.]

what if u were given a point and foci is it possible to make it into an equation?

[arushibhatia]

Thank you so much!! I might actually do well in this unit thanks to you :)

[ersonnatividad]

Mr . MClogan please help me my homework

here

Center at (-2, 3 ); major axis is horizontal; passing through (1, 4) and (2, 3)

[Dawnwar]

omg ur the goat this help me so much i might not fail precalc