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What is the center of the hyperbola x2−y2−49=0x^2 - y^2 - 49 = 0?\newline(_,_)(\_,\_)

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Q. What is the center of the hyperbola x2−y2−49=0x^2 - y^2 - 49 = 0?\newline(_,_)(\_,\_)
  1. Write Equation: Write the given equation x2−y2−49=0x^2 - y^2 - 49 = 0. Move the constant term to the right side to set the equation equal to a positive constant. x2−y2+49−49=49x^2 - y^2 + 49 - 49 = 49 x2−y2=49x^2 - y^2 = 49
  2. Move Constant Term: Convert the equation into the standard form of a hyperbola.\newlineDivide both sides of the equation by 4949.\newlinex249−y249=4949\frac{x^2}{49} - \frac{y^2}{49} = \frac{49}{49}\newlinex249−y249=1\frac{x^2}{49} - \frac{y^2}{49} = 1
  3. Convert to Standard Form: 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.\newlineOur equation x2/49−y2/49=1x^2/49 - y^2/49 = 1 can be rewritten as (x−0)2/49−(y−0)2/49=1(x - 0)^2/49 - (y - 0)^2/49 = 1.\newlineHere, h=0h = 0 and k=0k = 0.\newlineCenter of the hyperbola: (0,0)(0, 0)

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