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What is the length of the transverse axis of the hyperbola (x264)−(y236)=1(\frac{x^2}{64}) - (\frac{y^2}{36}) = 1?\newline______

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Find the length of the transverse or conjugate axes of a hyperbolaright chevron icon

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Q. What is the length of the transverse axis of the hyperbola (x264)−(y236)=1(\frac{x^2}{64}) - (\frac{y^2}{36}) = 1?\newline______
  1. Identify Orientation: Identify the orientation of the hyperbola.\newlineGiven equation: (x264−y236=1)(\frac{x^2}{64} - \frac{y^2}{36} = 1)\newlineSince the x2x^2 term is positive and comes first, this is a horizontal hyperbola.
  2. Determine 'a' Value: Determine the value of 'a' for the hyperbola.\newlineThe standard form of a horizontal hyperbola is (x2a2)−(y2b2)=1(\frac{x^2}{a^2}) - (\frac{y^2}{b^2}) = 1.\newlineComparing this with the given equation (x264)−(y236)=1(\frac{x^2}{64}) - (\frac{y^2}{36}) = 1, we find that a2=64a^2 = 64.\newlineTherefore, a=64=8a = \sqrt{64} = 8.
  3. Calculate Transverse Axis Length: Calculate the length of the transverse axis.\newlineFor a hyperbola, the length of the transverse axis is given by 2a2a.\newlineSince we found that a=8a = 8, the length of the transverse axis is 2×8=162 \times 8 = 16.

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