An ellipse has vertices along the major axis at (0, 1) and (0, −9). the foci of the ellipse are located at (0, −1) and (0, −7). the equation of the ellipse is in the form below.

The equation of the ellipse is required.

The required equation is

It can be see that the major axis is parallel to the y axis.

The major axis points are

Subtracting the equations

The foci are

Subtracting the equations

Foci is given by

The equation is

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So, with those points provided, notice the vertices are lying along the y-axis, check the picture below, thus is a vertical ellipse.

now, the center is half-way between the vertices, therefore it'd be at 0, -4, like in the picture in red.

the distance from the center to either foci, is "c", and that's c = 3.

the "a" component of the major axis is 5 units, now let's find the "b" component,