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What is the center of the hyperbola x2−4y2=36x^2 - 4y^2 = 36?\newline(_,_)(\_,\_)

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Q. What is the center of the hyperbola x2−4y2=36x^2 - 4y^2 = 36?\newline(_,_)(\_,\_)
  1. Prepare for Standard Form: x2−4y2=36x^2 - 4y^2 = 36\newlineMove the constant term to the right side to prepare the equation for standard form.\newlinex2−4y2−36+36=36x^2 - 4y^2 - 36 + 36 = 36\newlinex2−4y2=36x^2 - 4y^2 = 36
  2. Convert to Standard Form: x2−4y2=36x^2 - 4y^2 = 36\newlineConvert the equation into standard form by dividing both sides by 3636.\newlinex236−4y236=3636\frac{x^2}{36} - \frac{4y^2}{36} = \frac{36}{36}\newlinex2/36−y2/9=1x^2/36 - y^2/9 = 1
  3. Find Center of Hyperbola: x236−y29=1\frac{x^2}{36} - \frac{y^2}{9} = 1\newlineFind 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 for a horizontal hyperbola, or (y−k)2/a2−(x−h)2/b2=1(y - k)^2/a^2 - (x - h)^2/b^2 = 1 for a vertical hyperbola. In this case, we have a horizontal hyperbola with h=0h = 0 and k=0k = 0.\newlineCenter of the hyperbola: (0,0)(0, 0)

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