Given the vertices and foci, write the standard equation of an ellipse

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.
When given the two foci of the ellipse, the center of the ellipse is halfway between the two foci. 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. Using the pythagoras identity for the relationship between the focal length (distance between the center and the foci) and the radius, we can obtain the minor radius.
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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So is h and k 0 because its not the vertical axis? Also if the points on the vertices and the foci were h and k, how would the problem look and why?

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Hi.. How about if the vertices value is higher than the foci?

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Where did we get c^2 from though?

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I have a question. So is the base equation for getting the equation for an ellipse is (x-h)^2/a^2 + (y-k)^2/b^2 = 1 right?

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Nice work!. kindly help with this one. Given that f1(0,2) and f2(0,-2) are the foci of an ellipse which passes through the points Q(3,2), Find the equation of the ellipse.

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[@someonerandom1010]

I really enjoyed the video, but i have a question of my own. I was hoping you'd be able to take the time out of your day to answer is. I have a Center at (3,2) and V1 is (3,6) V3 is (-4,2). Write the equation of the ellipse.

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I'm taking precalculus on Khan Academy. Sal Khan is a great teacher but sometimes its difficult to understand all the problems that he teaches. I couldn't follow Sal Khan on this foci and vertices, it was very confusing. But this video is very simple and easy to understand. Thank you so much.

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what if like this The foci have coordinates (±√5,0) and a vertex at (1,0).

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How did you know the center was at the origin?

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Could you show me a video of Write an equation for an ellipse with foci (0, +4) and co-vertices (+ 2, 0).

[@brianmclogan]

search my channel with those words, have plenty of videos for that

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Master how to write the equation of an ellipse given foci, vertices and co vertices center at origin

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what formula to use when it is vertical? F(3,0) and V(6,0)

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(x-h)^2=4p(y-k)

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Do you have a video explaining how to do this when the center isn't (0, 0)?

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+Jack Snedegar plenty of them, you just have to search through my channel

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Found one, thanks!

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What do I do if I get a b^2 = 11. Do i need to squared it to become 3.3? or that is it?

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yes but I would leave it in radical form, remember the +/- sqrt(11)

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for an ellipse in standard form we want to be equal to one

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