Find the standard form of the equation of the ellipse and gi

Find the standard form of the equation of the ellipse and give the location of its foci. Type the standard form of the equation. (Type an equation. Simplify your answer.) Type the locations of the foci. (Type ordered pairs. Use a comma to separate answers. answers.)

Solution

Solution:

The center is (0,0) and the major axis is vertical, so standard form is
x²/b² + y²/a²= 1

The major axis of this ellipse is vertical and is the red segment from (7,0) to (-7,0)

The center of this ellipse is the origin since (0,0) is the midpoint of the major axis

The value of a = 7 and b = 6

x²/36 + y²/49= 1

Then c²= 49-36= 13
And c= sqrt(13)

The foci are on the major axis, and c units from the center. So in this case, they are actually on the y axis,

not the x.
Then the foci are (0, sqrt(13)) and (0,-sqrt(13))