Question

Find the vertices of the hyperbola with equation: (x-1)^2 - (y+2)^2 = 1

Answer 1

does anyone know how to do this?

Answer 2

the hyper has vertexes along the axis that is positive in the equation; for this one that means the x axis.

given that there are no denominatiors showing, we can determine that the distance from the center to a vertex is gonna be sqrt(1)

the center is clued in by the numbers that modify x and y; in this case -1 and +2. the center is the opposite of these numbers.

center = -(-1,2) = (1,-2)

since we want to move alone the x part; a distance of 1 each way we can determine the vertexes as: (1+1, 2) and (1-1, 2)