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Write the equation in standard form for the hyperbola x2−y2=64x^2 - y^2 = 64.\newline______

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Q. Write the equation in standard form for the hyperbola x2−y2=64x^2 - y^2 = 64.\newline______
  1. Identify equation and goal: Identify the given equation and the goal to write it in standard form.\newlineGiven equation: x2−y2=64x^2 - y^2 = 64\newlineGoal: Write in standard form for a hyperbola.
  2. Recognize standard form: Recognize the standard form of a hyperbola.\newlineThe standard form of a hyperbola with a horizontal transverse axis is (x2a2)−(y2b2)=1(\frac{x^2}{a^2}) - (\frac{y^2}{b^2}) = 1, where aa and bb are real numbers.
  3. Divide equation by 6464: Divide both sides of the equation by 6464 to get the equation in standard form.\newline(x264)−(y264)=6464(\frac{x^2}{64}) - (\frac{y^2}{64}) = \frac{64}{64}\newlineSimplify the right side of the equation to get 11.\newline(x264)−(y264)=1(\frac{x^2}{64}) - (\frac{y^2}{64}) = 1

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