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What is the center of the hyperbola x2−y2−9=0x^2 - y^2 - 9 = 0?\newline(_,_)(\_,\_)

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Q. What is the center of the hyperbola x2−y2−9=0x^2 - y^2 - 9 = 0?\newline(_,_)(\_,\_)
  1. Rewrite Equation: Rewrite the equation to isolate the constant term on one side.\newlineMove the constant term to the right side of the equation.\newlinex2−y2−9+9=9x^2 - y^2 - 9 + 9 = 9\newlinex2−y2=9x^2 - y^2 = 9
  2. Standard Form Conversion: Convert the equation into the standard form of a hyperbola.\newlineDivide both sides of the equation by 99 to get the standard form.\newlinex29−y29=99\frac{x^2}{9} - \frac{y^2}{9} = \frac{9}{9}\newlinex29−y29=1\frac{x^2}{9} - \frac{y^2}{9} = 1
  3. Identify Center: Identify the center of the hyperbola.\newlineThe standard form of a hyperbola is (x−h)2/a2−(y−k)2/b2=1(x-h)^2/a^2 - (y-k)^2/b^2 = 1, where (h,k)(h, k) is the center.\newlineIn our equation, x2/9−y2/9=1x^2/9 - y^2/9 = 1, we can see that h=0h = 0 and k=0k = 0.\newlineCenter of the hyperbola: (0,0)(0, 0)

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