Answer to Question #247350 in Analytic Geometry for Shabnam

Question

Write the coordinates for the center of the hyperbola:

((y - 2) ^ 2)/16 - ((x + 1) ^ 2)/144 = 1

Answer 1

Solution.

Equation of hyperbola in general form:

$$\frac{(x-m)^{2}}{a^{2}}-\frac{(y-n)^{2}}{b^{2}}=1$$

where

m, n – coordinates of the center of the hyperbola

$a, b \in \mathbb {R}$

The given hyperbola in the problem is rotated to $\frac{\pi}{2}$:

$$\frac{(y-2)^{2}}{4^{2}}-\frac{(x+1)^{2}}{12^{2}}=1$$

Figure 1. Hyperbola rotated by $\frac{\pi}{2}$

$\begin{matrix} m = -1 \\ n = 2 \end{matrix} \implies$ Hyperbola with center (-1, 2)

Answer: (-1, 2)