Question

The equation (y-8)^2/49 + (x -1)^2/36 = 1 represents an ellipse. Which points are the approximate locations of the foci of the ellipse? Round to the nearest tenth.

Answer 1

(1,4.4) and (1,11.6)

Explanation:

Answer 2

The points that are the approximate locations of the foci of the ellipse are (0,√13) and (0,-√13) or, what is the same, (0,3.60) and (0,-3.60)

Explanation:

The equation
`((y-8)^(2) )/(49) +((x-1)^(2) )/(36) =1` follows the following form of representation of an ellipse:
`((y-y_(0) )^(2) )/(a^(2) ) +((x-x_(0) )^(2) )/(b^(2) ) =1`

where x₀ and y₀ are the values ​​of x and y in the center of the ellipce and a nab b are the values ​​of the major and minor semiaxis, respectively. So the major axis is vertical in this case.

Being c the focal length, the relationship between the focal length and the semi-axes is:
`a^(2) =b^(2) +c^(2)` The foci are located on the major axis

In this case: 49=36+c²

Solving: c²=49-36

c²=13

c=√13 ≅ 3.60

So, the points that are the approximate locations of the foci of the ellipse are (0,√13) and (0,-√13) or, what is the same, (0,3.60) and (0,-3.60)