Question

Write the coordinates for the center of the hyperbola:(x−2)²/36−(y−1)²/64=1.

a) (2,1)
b) (1,2)
c) (2,−1)
d) (−2,1)

Answer 1

The center of the hyperbola given by the equation (x−2)²/36−(y−1)²/64=1 is at the coordinates (2,1). The correct option is (a).

Step-by-step explanation:

The student has asked for the coordinates of the center of a hyperbola given by the equation (x−2)²/36−(y−1)²/64=1. This is a standard form of a hyperbola where the center coordinates (h,k) are evident as the values that are subtracted from x and y in the equation. Hence, in this equation, the center is at (h,k) = (2,1).

To further clarify, the general form for the equation of a hyperbola centered at (h,k) is −(x−h)²/a² − (y−k)²/b² = ±1, where 'a' and 'b' are constants. Given that the equation provided is already in this general form, we can directly read off the center's coordinates, which is option a) (2,1).