Question

HELP PLEASE
the ellipse having foci located at (3,1) and (7,1) and a major axis of length 10.

What are the coordinates of the vertices?

What is the length of the minor axis?

Find the eccentricity of the ellipse.

Answer 1

help please?

Answer 2

...?

Answer 3

The center is halfway between the foci, so it has to be at (5,1)
The semimajor axis is half of the major axis so it's 5
and it passes from the center through the foci to the vertex
The vertices are 5 to the left and right of (5,1), making them (0,1) and (10,1)

Answer 4

Thank You, Thank you :)

Answer 5

to solve for b (the semiminor axis), you need to know a and c
you know a as 5, and c is the distance from center to foci, which is 2
the formula to solve for b is a^2-b^2=c^2
if you plug in and solve, b is sqrt(21), making the minor axis 2sqrt(21)