Write the equation of an ellipse given the center, vertex and focus

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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[idlesuggest]

This guy taught me geometry better than my teacher ever did...

[jhoemariemacayan]

What formula to be used if it is horizontal?

[bemerosecaroline]

But what if center is not given only vertex foci and length of minor axis

[alinujvisera]

But what if the center is (-2, 4) the vertex is (3, 4) and the focus is (4, 4) ? your example is at (0, 0) then the vertex and focus is at y-intercept.