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What is the center of the hyperbola x2−y2−25=0x^2 - y^2 - 25 = 0?\newline(_,_)(\_,\_)

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Q. What is the center of the hyperbola x2−y2−25=0x^2 - y^2 - 25 = 0?\newline(_,_)(\_,\_)
  1. Write Equation: Write the given equation x2−y2−25=0x^2 - y^2 - 25 = 0. Move the constant term to the right side to set the equation equal to a constant. x2−y2=25x^2 - y^2 = 25
  2. Convert to Standard Form: Convert the equation into the standard form of a hyperbola.\newlineDivide both sides of the equation by 2525 to get 11 on the right side.\newlinex225−y225=2525\frac{x^2}{25} - \frac{y^2}{25} = \frac{25}{25}\newlineSimplify the equation to get the standard form.\newlinex225−y225=1\frac{x^2}{25} - \frac{y^2}{25} = 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 x2/25−y2/25=1x^2/25 - y^2/25 = 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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