Write an equation for an ellipse if the endpoints of the major axis are at (1,6) and (1,-6) and the endpoints of the minor axis are at (5,0) and (-3,0).

My answer is y^2/36 + (x-1)^2/16 = 1.

Is this correct?

Thanks.

It looks like the answer I posted yesterday. Are you asking for second opinions?

well, the center is at (1,0) and the major axis is up and down

Half the height is 6 and half the width is 4
(y-0)^2/6^2 + (x-1)^2/4^2 = 1
so I agree.

hmmm, we often agree :)

It was a different problem, worked in the same manner. I just wasn't sure if I worked it correctly.

Yes, your answer is correct. The equation you provided is indeed the equation of an ellipse.

To explain how to arrive at this equation, we can start by understanding the general form of the equation for an ellipse centered at the point (h, k):

((x-h)^2)/a^2 + ((y-k)^2)/b^2 = 1

In your case, the center of the ellipse is given by the points (1, 0) since the major axis is vertical, and the midpoint between the endpoints of the major axis is at (1, 0).

To determine the values of a and b, we need to find the lengths of the major and minor axes.

The length of the major axis is the distance between the endpoints (1, 6) and (1, -6), which is 6 - (-6) = 12. Therefore, a = 6.

The length of the minor axis is the distance between the endpoints (5, 0) and (-3, 0), which is 5 - (-3) = 8. Therefore, b = 4.

Now we can substitute these values into the general equation of the ellipse:

((x-1)^2)/6^2 + (y-0)^2/4^2 = 1

Simplifying,

(x-1)^2/36 + y^2/16 = 1

So your answer, y^2/36 + (x-1)^2/16 = 1, is correct.