Question
What is the foci for the ellipse x^2/9+(y+5)^2/25=1
Answers
GPT 3.5
The foci of an ellipse can be found using the formula c = √(a^2 - b^2), where a is the length of the major axis and b is the length of the minor axis.
In this case, the major axis is along the y-axis, so a = 5 and b = 3 (since 5 is the square root of 25 and 3 is the square root of 9).
Calculating the value of c:
c = √(5^2 - 3^2)
c = √(25 - 9)
c = √16
c = 4
Therefore, the foci for the given ellipse are (0, -5 + 4) = (0, -1) and (0, -5 - 4) = (0, -9).
In this case, the major axis is along the y-axis, so a = 5 and b = 3 (since 5 is the square root of 25 and 3 is the square root of 9).
Calculating the value of c:
c = √(5^2 - 3^2)
c = √(25 - 9)
c = √16
c = 4
Therefore, the foci for the given ellipse are (0, -5 + 4) = (0, -1) and (0, -5 - 4) = (0, -9).