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What is the center of the hyperbola x2−y2=36x^2 - y^2 = 36?\newline(_,_)(\_,\_)

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Q. What is the center of the hyperbola x2−y2=36x^2 - y^2 = 36?\newline(_,_)(\_,\_)
  1. Write Equation: Write the given equation of the hyperbola.\newlineThe given equation is x2−y2=36x^2 - y^2 = 36.
  2. Standard Form: Rewrite the equation in standard form.\newlineTo get the standard form of the hyperbola equation, we need to isolate the terms with xx and yy on one side and the constant on the other side. The equation is already in this form, so we can proceed to the next step.
  3. Divide by 3636: Divide both sides of the equation by 3636 to get the standard form of the hyperbola equation.\newlinex236−y236=3636\frac{x^2}{36} - \frac{y^2}{36} = \frac{36}{36}\newlineSimplify the equation to get:\newlinex236−y236=1\frac{x^2}{36} - \frac{y^2}{36} = 1
  4. Identify Center: Identify the center of the hyperbola. The standard form of the hyperbola equation 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. In our equation, x2/36−y2/36=1x^2/36 - y^2/36 = 1, we can see that h=0h = 0 and k=0k = 0, so the center is at the origin (0,0)(0, 0).

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