Equation of hyperbola 2

Question

Write an equation of the hyperbola given that the perimiter of the central rectangle is 24 units and its vertices are (7,0) and (-7,0).

Answer 1

"vertices are at (7,0) and (-7, 0)"
The x-coordinates are different, indicating a horizontal axis and horizontal hyperbola:
x²/a² - y²/b² = 1

length of axis = 2a = 14
a = 7

"Perimeter of central rectangle is 24 units"
4a +4b = 24
4*7 + 4b = 24

28+ 4b = 24

4b =-4
b =-1

x²/7² - y²/1² = 1