Question
Given the hyperbola find the coordinates of the center and vertices x^2-100y^2=100
Answers
Answered by
GPT 3.5
To find the center and vertices of the hyperbola with the equation x^2 - 100y^2 = 100, we first need to rewrite the equation in standard form.
Divide both sides of the equation by 100 to simplify:
x^2 / 100 - y^2 = 1
Now, we can see that this is a hyperbola with a horizontal transverse axis because x^2 is positive and y^2 is negative. Next, we find the center by taking the square root of the denominators:
Center: (0, 0)
To find the vertices, we need to find the value of a, which is the square root of the positive term, so it is 10:
a = 10
Now, we can find the equation of the hyperbola's transverse axis:
Vertices: (±a, 0)
Vertices: (±10, 0)
Therefore, the center of the hyperbola is (0, 0) and the vertices are (±10, 0).
Divide both sides of the equation by 100 to simplify:
x^2 / 100 - y^2 = 1
Now, we can see that this is a hyperbola with a horizontal transverse axis because x^2 is positive and y^2 is negative. Next, we find the center by taking the square root of the denominators:
Center: (0, 0)
To find the vertices, we need to find the value of a, which is the square root of the positive term, so it is 10:
a = 10
Now, we can find the equation of the hyperbola's transverse axis:
Vertices: (±a, 0)
Vertices: (±10, 0)
Therefore, the center of the hyperbola is (0, 0) and the vertices are (±10, 0).