Question

What is the sum of the focal radii? (x-4)²/36+(y+2)²/16=1

Answer 1

It's the same as teh major axis, 2a

Answer 2

thanks! do you know what the coordinates of the 4 vertices would be? @mathstudent55

Answer 3

What are the lengths of the major axis and minor axis?

Answer 4

major=12 minor=8

Answer 5

If the ellipse were centered at (0, 0), the graph shows the points. But because of x - 4 and y + 2 in the equation, the -4 and + 2 show a translation.

Answer 6

In the standard equation, you have x - h and y - k, for an ellipse centered at (h, k). Since here you have x - 4 and y + 2, that means the center is (4, -2).
Now look at the ellipse in my graph. The vertices are:
(6, 0), (-6, 0), (0, 4), (0, -4) with center at (0, 0)
Since you have center at (4, -2), you must add 4 and subtract 2 from each x- and y-coordinate, respectively, of the vertices with center (0, 0)

Answer 7

thank you so much, i understand it so much better now. really appreciate it. can you help me with one more thing? do you know what the eccentricity of this ellipse would be? i have no idea how to get that @mathstudent55