Question

9x^2 - y^2 - 90x + 4y + 140= 01. does the ellipse open horizontally or vertically?2. give the coordinates of the right vertex3. give the coordinates of the left vertex4. give the coordinates of the right focus(round to the nearest hundredths)5. give the coordinates of the left focus(round to the nearest hundredths)6. give the eccentricity

Answer 1

the function is:

`9x^2-y^2-90x+4y+140=0`

We can graph the function to be sure:

1) In this case the ellipse open vertically because there is a contraction in the x axis.

2) The right vertex is in the coordinate (8,2)

3) the eft vertex is in the coordinate (2,2)

4) the right focus is in the coordinate (14.5,2)

5) the left focus is in the coordinate (-4.5,2)

6) and the eccentricity is the divition between the distance of the center to the vertex by the distance of the center to the focus so:

`e=(9.5)/(3)=3.16`