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).
To write the equation of an ellipse, we need to use the general form of the equation for an ellipse centered at the origin:
x^2/a^2 + y^2/b^2 = 1
where "a" is half the length of the major axis, and "b" is half the length of the minor axis.
First, let's find the values of "a" and "b".
The length of the major axis is the distance between the endpoints (1,6) and (1,-6), which is equal to 12. Since the major axis has to be symmetric with respect to the center, "a" is half of this length, so a = 12/2 = 6.
The length of the minor axis is the distance between the endpoints (5,0) and (-3,0), which is equal to 8. Similarly, "b" is half of this length, so b = 8/2 = 4.
Now, we can plug these values into the equation:
x^2/6^2 + y^2/4^2 = 1
Simplifying, we get the final equation:
x^2/36 + y^2/16 = 1
So, the equation of the ellipse with the given endpoints is x^2/36 + y^2/16 = 1.