Question

The vertices for the hyperbola (x-2)^2/36-(y+1)^2/64=1 are (2,5) and (2,-7) true or false

Answer 1

\[\frac{ (x-2)^2 }{ 36 }-\frac{ (y+1) }{ 64}=1\]

Answer 2

and is it and equation of a horizontal hyperbola?

Answer 3

It is a horizontal hyperbola because it corresponds to the standard equation for a horizontal hyperbola: \(\Large \frac{(x-h)^2}{a^2} - \frac{(y-k)^2}{b^2} = 1\)

Answer 4

The center of the hyperbola is (h,k). Here the center is (2, -1).
The vertex will lie in the same horizontal line as the center and therefore, the y-coordinate will be the same as the y-coordinate of the center (2,-1) which is -1.
The given points (2,5) and (2,-7) do not have the y value of -1 and therefore they are NOT the vertices.