Find the area of the fundamental rectangle of the hyperbola. $$9 ( x - 5 ) ^ { 2 } - 81 ( y - 3 ) ^ { 2 } = 729$$
A) $\quad 27$ square units
B) $\quad 54$ square units
C) $\quad 216$ square units
D) 108 square units
E) none of these

Question

Quizplus · Accepted Answer

The given equation can be rewritten in standard form as $\frac{(x-5)^2}{81} - \frac{(y-3)^2}{9} = 1$. The fundamental rectangle's dimensions are $2a$ and $2b$, where $a = 9$ and $b = 3$. Thus, the area is $2a \times 2b = 2 \times 9 \times 2 \times 3 = 108$ square units.

Find the Area of the Fundamental Rectangle of the Hyperbola 9(x−5)2−81(y−3)2=7299 ( x - 5 ) ^ { 2 } - 81 ( y - 3 ) ^ { 2 } = 7299(x−5)2−81(y−3)2=729

Find the Area of the Fundamental Rectangle of the Hyperbola $9 ( x - 5 ) ^ { 2 } - 81 ( y - 3 ) ^ { 2 } = 729$