Find the foci of the following hyperbola. Be sure to show all work, and write your answer as an ordered pair in simplest radical form x^2/36 - y^2/225=1
why did you post this twice?
I apologize, as an AI language model, I did not realize that I had already posted the solution to this problem in a previous response.
To find the foci of the hyperbola, we need to determine the values of "a" and "b". The equation of the hyperbola is given as:
x^2/36 - y^2/225 = 1
We can rewrite the equation in standard form as:
(x - h)^2/a^2 - (y - k)^2/b^2 = 1
Comparing this equation with the given equation, we can determine the values of "h", "k", "a", and "b". In this case, "h" and "k" are both equal to zero.
a^2 = 36
a = √36
a = 6
b^2 = 225
b = √225
b = 15
The values of "a" and "b" are now known. The coordinates of the foci can be found using the formula:
c = √(a^2 + b^2)
c = √(6^2 + 15^2)
c = √(36 + 225)
c = √261
Therefore, the foci of the hyperbola are located at the coordinates (0, ±√261).
To find the foci of a hyperbola, we need to use the equation of the hyperbola and some key properties of hyperbolas.
The equation of the hyperbola is given as:
(x^2 / a^2) - (y^2 / b^2) = 1
Comparing it to the given equation:
(x^2 / 36) - (y^2 / 225) = 1
We can observe that a^2 = 36 and b^2 = 225.
Now, let's find the value of c^2 (c squared) using the equation c^2 = a^2 + b^2.
c^2 = 36 + 225 = 261
Next, we need to find the square root of c^2 to get c:
c = √261
For a hyperbola, the foci are located at (±c, 0). Therefore, the foci are:
Foci = (±√261, 0)
Hence, the foci of the given hyperbola are (√261, 0) and (-√261, 0).