Question
What are the foci of the ellipse given by the equation 25x^2 + 16y^2= 400?
(± 3, 0)
(± 3, 0)
(± 9, 0)
(± 9, 0)
(0, ± 3)
(0, ± 3)
(0, ± 9)
(± 3, 0)
(± 3, 0)
(± 9, 0)
(± 9, 0)
(0, ± 3)
(0, ± 3)
(0, ± 9)
Answers
GPT 3.5
The standard form equation of an ellipse is (x-h)^2/a^2 + (y-k)^2/b^2 = 1, where (h,k) is the center of the ellipse, a is the distance from the center to a vertex along the x-axis, and b is the distance from the center to a vertex along the y-axis.
Given the equation 25x^2 + 16y^2 = 400, we can rewrite it as (x^2/16) + (y^2/25) = 1 by dividing by 400 on both sides.
Comparing with the standard form equation, we see that a = 4 and b = 5. The center is at (0,0).
For an ellipse, the foci are given by the formula c^2 = a^2 - b^2. In this case c^2 = 16 - 25 = -9. Taking the absolute value, we find that c = 3.
Therefore, the foci are given by (± 3, 0).
Given the equation 25x^2 + 16y^2 = 400, we can rewrite it as (x^2/16) + (y^2/25) = 1 by dividing by 400 on both sides.
Comparing with the standard form equation, we see that a = 4 and b = 5. The center is at (0,0).
For an ellipse, the foci are given by the formula c^2 = a^2 - b^2. In this case c^2 = 16 - 25 = -9. Taking the absolute value, we find that c = 3.
Therefore, the foci are given by (± 3, 0).