How to write the equation of an ellipse given the vertices and foci

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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[@ShraotiLaj]

Can you please explain how to find the vertex like (-2,0) at this video?

[@eeshananand2053]

I've learned more from him. Then I've learned from my teacher this entire year.

[@sunshineshining7850]

my lord and savior helping me out even in 2018. for all you kerr students, i hope you find this video and let it save your ass.

[@brianmclogan]

appreciate it and happy to be able to help you out!