Write the equation of an ellipse given the foci 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.
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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[@jadenlawrence7807]

I know this is old but at the end when he subtracts 64 from 25 he wrote -41 but it would be -39. Very helpful video it’s just I have this same question on my study guide so I was super confused while watching that part.

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Sir if foci (3,0) ,(5,0) and vertex (1,0) then how to find equation of ellipse

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[@brianmclogan]

you are very welcome Allison! happy to be able to help

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[@dwatson1470]

Do you do the same if your given the foci and the co vertices

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[@iamwhoiam5921]

Sir is it ok if the situation is 81=169-b² will be b²= 169-81?

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What do if do if in my foci, I have a square root? Like (-7 ± sqrt(119), -5)

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[@seuji]

Thank you for sir.

[@bryonsegunto8901]

Sir, I've tried your way and it doesn't work if the center is not in 0,0

[@brianmclogan]

it does you just have to adjust to the new center (h,k)

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[@MentallyHygienic]

Shouldn't it be sqrt(39) if b squared is 39?

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[@brianmclogan]

You are very welcome!!

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What if center is not (0,0)? What will happen to the signs?

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[@sinichikudo6528]

Why did you subtract 64 to 25?. I think you should divide 64 to 25 to cancel both of them

[@brianmclogan]

you will divide 64 when it is being multiplying by 64, in this case that is not happening 64 is being added to b^2 not multiplied

[@sinichikudo6528]

Ohhh. Okay thanks. Do you have any video about vertical ellipse with a center, vertice, foci?

[@ninoanthonyonate3571]

How did he get the -41? answer pls

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keep watching, he made a mistake and fixed it later on

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what are h and k though?

[@brianmclogan]

just real numbers

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@@brianmclogan The x and y values for the center right?

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[@elaizamaeromaniez9211]

b^2 is 36 which is b=6

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