Question

Find the center, vertices, and foci of the ellipse with equation x squared divided by one hundred plus y squared divided by thirty six = 1.

Answer 1

The equation of an ellipse is:
(x-h)²/a² + (y-k)²/b², where h, k are the coordinates of the center, a & b represent half of the major & minor axis respectively.
The given equation is:
x²/100 + y²/36 = 1.( a =10 and b = 6)

CENTER: Since h and k = 0, then the center of this ellipse is the origin (0,0)

VERTICES: a² = 100, → a = +10 and a = -10, then the right vertex is (10,0) and the left vertex is (-10,0)

FOCI: The distance "c" from the center to the focus is given by the following:

c² = a² - b²

c² = 100 - 36 = 64  and c = +8 and - 8

The coordinate of the right focus F₁(8,0) and F₂(-8,0) for the left focus