Question

I need help trying to solve the problem for each letter.

Answer 1

`(\left(x-2\right)^(2))/(9^(2))+(\left(y+4\right)^(2))/(6^(2))=1`

1) Looking at the graph we can trace a line from the largest point to the right and to the largest point to the left. This will help us to find the Center of the Ellipse:

So, the intersection point of those axes will point out the center of the ellipse. So the center is at (2,-4) Therefore the coordinates h=2 and k=-4

2) Note for the major and minor axis we can do the following:

Minor axis b:

Counting in the graph from the center to the outline of that ellipse

2-(-4)=6 so the b coordinate from that minor axis is b=6

Major axis a

Counting the major axis, we can tell that from the center to the outline to the right and from the center to the outline to the left we can tell that there is 9 units to the right as well as to the left.

3) Thus, the answer is:

`(\left(x-2\right)^(2))/(9^(2))+(\left(y+4\right)^(2))/(6^(2))=1`