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What is the center of the hyperbola 4x2−y2−36=04x^2 - y^2 - 36 = 0?\newline(_,_)(\_,\_)

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Q. What is the center of the hyperbola 4x2−y2−36=04x^2 - y^2 - 36 = 0?\newline(_,_)(\_,\_)
  1. Move constant term: 4x2−y2−36=04x^2 - y^2 - 36 = 0\newlineMove the constant term to the right side of the equation.\newline4x2−y2=364x^2 - y^2 = 36
  2. Convert to standard form: 4x2−y2=364x^2 - y^2 = 36\newlineConvert the equation into standard form by dividing both sides by 3636.\newline4x236−y236=3636\frac{4x^2}{36} - \frac{y^2}{36} = \frac{36}{36}\newlineSimplify the fractions.\newlinex29−y236=1\frac{x^2}{9} - \frac{y^2}{36} = 1
  3. Simplify fractions: x29−y236=1\frac{x^2}{9} - \frac{y^2}{36} = 1\newlineIdentify the center of the hyperbola.\newlineThe equation is now in the standard form (x−h)2/a2−(y−k)2/b2=1(x - h)^2/a^2 - (y - k)^2/b^2 = 1, where hh and kk are the xx and yy coordinates of the center, respectively. Since there are no (x−h)(x - h) or (y−k)(y - k) terms, hh and kk are both (x−h)2/a2−(y−k)2/b2=1(x - h)^2/a^2 - (y - k)^2/b^2 = 100.\newlineCenter of the hyperbola: (x−h)2/a2−(y−k)2/b2=1(x - h)^2/a^2 - (y - k)^2/b^2 = 111

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