Answer to Question #247350 in Analytic Geometry for Shabnam

Question #247350

Write the coordinates for the center of the hyperbola:

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


1
Expert's answer
2021-10-06T16:51:30-0400

Solution.

Equation of hyperbola in general form:


(xm)2a2(yn)2b2=1\frac{(x-m)^{2}}{a^{2}}-\frac{(y-n)^{2}}{b^{2}}=1


where

m, n – coordinates of the center of the hyperbola

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


The given hyperbola in the problem is rotated to π2\frac{\pi}{2}:

(y2)242(x+1)2122=1\frac{(y-2)^{2}}{4^{2}}-\frac{(x+1)^{2}}{12^{2}}=1



Figure 1. Hyperbola rotated by π2\frac{\pi}{2}

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


Answer: (-1, 2)


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