To determine the foci of the ellipse given by the equation x²/49 + y²/64 = 1, we first need to identify the values of a² and b² from the standard form of the ellipse equation.
This equation can be rewritten in the standard form as:
x²/a² + y²/b² = 1
From x²/49, we see that a² = 49. Thus, a = √49 = 7.
From y²/64, we see that b² = 64. Thus, b = √64 = 8.
For an ellipse, the distance to the foci is given by the formula:
c = √(b² – a²)
Substituting our values:
c = √(64 – 49) = √15
The foci of the ellipse are located along the major axis, which in this case is along the y-axis since b > a. The coordinates of the foci, therefore, are:
(0, ±c) = (0, ±√15)
Thus, the foci of the ellipse x²/49 + y²/64 = 1 are at the points (0, √15) and (0, -√15).