Question

question 2 of 10
write the coordinates for the center of the hyperbola:
\\(\frac{(x - 2)^2}{36}-\frac{(y + 1)^2}{64}=1\\)

Explanation:

Step1: Recall hyperbola standard form

The standard - form of a hyperbola is $\frac{(x - h)^2}{a^2}-\frac{(y - k)^2}{b^2}=1$ for a hyperbola that opens left and right, and its center is at the point $(h,k)$.

Step2: Identify $h$ and $k$

For the given hyperbola $\frac{(x - 2)^2}{36}-\frac{(y+1)^2}{64}=1$, we can rewrite the equation as $\frac{(x - 2)^2}{36}-\frac{(y-(-1))^2}{64}=1$. Here, $h = 2$ and $k=-1$.

Answer:

$(2,-1)$