Question

Write the coordinates for the center of the hyperbola (y-2)^2/16-(x 1)^2/144=1

Answer 1

The center of the hyperbola given by the equation
`(y-2)^2/16 - (x+1)^2/144 = 1`

Step-by-step explanation:

The question asks for the coordinates of the center of a hyperbola represented by the equation
`(y-2)^2/16 - (x+1)^2/144 = 1` where (h, k) are the coordinates of the center of the hyperbola. Based on this information, the center of the hyperbola can be identified directly from the equation as the point with coordinates (h, k), which is the point (-1, 2). This means that the x-coordinate is -1 and the y-coordinate is 2.

Answer 2

The coordinates for the center of the hyperbola ((y-2)²/16 - (x-1)²/144 = 1) are (1, 2).

In the given equation, ((y-2)²/16 - (x-1)²/144 = 1), we can recognize that it is in the standard form of a hyperbola equation: (y-k)²/a² - (x-h)²/b² = 1). Here, (h, k) represents the center of the hyperbola. Comparing the equation to the standard form, we can see that (h = 1) and (k = 2), so the center of the hyperbola is at the point (1, 2).

To find the center, we need to isolate (y) and (x) terms and rearrange the equation to match the standard form. First, we move the constant on the right side:

(y-2)²/16 = (x-1)²/144} + 1

Now, we can see that (a² = 16) and (b² = 144). Taking the square root of these values, we get (a = 4) and (b = 12). The center of the hyperbola is located at the point (h, k), so (h = 1) and (k = 2). Thus, the center is at (1, 2).