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Write the equation in standard form for the hyperbola y2−9x2=144y^2 - 9x^2 = 144.\newline______

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Q. Write the equation in standard form for the hyperbola y2−9x2=144y^2 - 9x^2 = 144.\newline______
  1. Identify Operation: Identify the operation to write the equation in standard form.\newlineDivide both sides by 144144 to isolate the terms on the left side of the equation.\newlineOperation: Division
  2. Perform Division: Perform the division operation on the equation y2−9x2=144y^2 - 9x^2 = 144. Divide each term by 144144 to get the standard form of the hyperbola. y2144−9x2144=144144\frac{y^2}{144} - \frac{9x^2}{144} = \frac{144}{144}
  3. Simplify Equation: Simplify the equation obtained in Step 22.\newliney2/144−(9x2)/144=1y^2/144 - (9x^2)/144 = 1\newlineSince 9x2/1449x^2/144 can be simplified to x2/16x^2/16, the equation becomes:\newliney2/144−x2/16=1y^2/144 - x^2/16 = 1
  4. Write Final Equation: Write the final equation in standard form.\newlineThe standard form for a hyperbola is (y2/a2)−(x2/b2)=1(y^2/a^2) - (x^2/b^2) = 1, where 2a2a and 2b2b are the lengths of the transverse and conjugate axes, respectively.\newlineThus, the standard form of the given hyperbola is:\newliney2/144−x2/16=1y^2/144 - x^2/16 = 1

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