Question

Graph an ellipse with foci at (±4, 0) and a minor axis of length 6.

Answer 1

You can just explain the graph if you want

Answer 2

Hi Mito, the foci of an ellipse will always be on the major axis, not the minor axis. Therefore the major axis is the one along the x-axis, and the minor axis will by along the y axis.
So your ellipse will be centered around (0,0) with a maximum height of 6 and a minimum of -6 at the y-intercepts (0,+-6)

Answer 3

Also, it is a property of an ellipse that \[r_1 +r_2 = 2a\]
so if we know a point (0,6). Then \[r_1 = r_2 = sqrt(6^2 + 4^2))= 2a therefore 2a = sqrt(52)\]
(2a is the length of the major axis)

Answer 4

Oops, Sorry Mitosuki, I just realized it says 6 is the length of the minor axis, not the minor radius. So it is the same , but only up to (0,3) and (0,-3)