SOLUTION: Write an equation for each ellipse. Center at (-3,6); major axis vertical, with length 10; C=2

Question 721364: Write an equation for each ellipse.
Center at (-3,6); major axis vertical, with length 10; C=2
Answer by jsmallt9(3759) (Show Source): You can put this solution on YOUR website!
The standard forms for the equation of a ellipse are:
for horizontal ellipses
and
for vertical ellipses
In these standard forms...

The "h" and "k" are the x and y coordinates of the center of the hyperbola.
The "a" is the distance from the center to a vertex on the major axis.
The "b" is the distance from the center to a vertex on the minor axis.

Since we've been told that the major axis is vertical, our ellipse is vertical. So from this point on, we will be using:

We know that the center is (-3, 6). So the h and k of the equation will be -3 and 6.
Since the length of the major axis is 10, the distance from the center to each vertex will be half of that, or 5. So a = 5.
To find "b" we will use the equation that connects the values of a, b and c in an ellipse:

(We ignore the negative square root since b is a distance.)
Now that we have the h, k, a and b values we can write the equation:

which simplifies to:

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