Write the equation of an ellipse given the vertices and co 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. When given the vertices of an ellipse, the major radius of an ellipse is the distance between the center of the ellipse and its vertices. When given the co-vertices of an ellipse, the minor radius of an ellipse is the distance between the center of the ellipse and its co-vertices.

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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[rockyk]

thanks so much you cleared everything up. YOU'RE A GREAT TEACHER

[alexfernando]

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[christianmarfil]

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[ravenashc]

Amazed at how you explained it so simply unlike my teacher, thank you so much!!

[g_buganterinaflor]

I love how you teach the lessons it gives me clarity. Thanks keep on doing things like this.

[mirandasheenamaed.]

Thank you for your videos, I really appreciate it and it helps me a lot, God bless!

[cessyanez]

Good day Sir, how about if there is only 1 point given for both the vertices and covertices? You really helped a lot Sir, thank you.

[rockyk]

can u please please PLEASE explain why you put a^2 below the y again. How do you know which is the a^2 and b^2.
in other words how did you know a^2 goes under y when b^2 normally goes under. and how do u know when to do that in a question. plz respond soon :)

[EstebanGomez-hmlc]

Hello! How would the procedure be if I have the vertices at (-2, -2) and (2, 2)? In other words, a diagonal ellipse or in any other direction than horizontal or vertical... Thanks!

[nallaaavi]

May I know, how did the sign changed in (x-h)² - to - (x+1)²...? Btw, I'm learning because of your videos. Thanks a lot, po✨

[cindyjincampus]

Hello sir! Is this the standard form of the equation? How about the general form?

[baluyotlover]

HOw did you know it was a vertical ellipse 😭😭😭 im confused