Write the equation for an ellipse give foci 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.

When given the two foci of the ellipse, the center of the ellipse is halfway between the two foci. 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. 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 major 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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[emmanuelgonzales]

you forgot to sq. the x-h anyways, thank you so much Sir!

[madelinekoehl]

you are my teacher and some other man is getting paid for it 😂

[lightryder]

Bro you just saved me your a real one fr

[cantrememberlekisname]

I and my classmates are so thankful for you, Sir. 😭

[bana-nice]

Sir your videos help me a lot!! And i am just wondering what to do if only a focus is given?

[eeshananand]

I'm learning more from him, than my teacher.

[rivlier]

What happens if the co vertices and foci length is both 16?

[mickasato]

Oh my goodness, thank you so much! I know how to do this now!

[arlenealilano]

An ellipse has a co-vertex at (–8, 9) and a foci at (4, 4). If the center of the ellipse is located below the given co-vertex, then what is the equation of the ellipse? please help sir, it's really confusing if there is only given 1 foci and covertex, how do I find it?

[rashanet]

Is this being taught at a high school or college of some sort? Was always curious