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What is the center of the hyperbola x2−y2−81=0x^2 - y^2 - 81 = 0?\newline(_,_)(\_,\_)

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Q. What is the center of the hyperbola x2−y2−81=0x^2 - y^2 - 81 = 0?\newline(_,_)(\_,\_)
  1. Write Equation: Write the given equation of the hyperbola.\newlineThe given equation is x2−y2−81=0x^2 - y^2 - 81 = 0.
  2. Move Constant Term: Move the constant term to the right side of the equation.\newlinex2−y2=81x^2 - y^2 = 81
  3. Convert to Standard Form: Convert the equation into the standard form of a hyperbola.\newlineDivide both sides of the equation by 8181 to get the standard form.\newlinex281−y281=8181\frac{x^2}{81} - \frac{y^2}{81} = \frac{81}{81}\newlinex281−y281=1\frac{x^2}{81} - \frac{y^2}{81} = 1
  4. Identify Center: Identify the center of the hyperbola.\newlineThe standard form of the equation 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 of the hyperbola.\newlineIn our equation, (x2)/81−(y2)/81=1(x^2)/81 - (y^2)/81 = 1, we can see that h=0h = 0 and k=0k = 0.\newlineTherefore, the center of the hyperbola is (0,0)(0, 0).

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