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Write the equation in standard form for the hyperbola 9y2−x2=369y^2 - x^2 = 36.\newline______

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Q. Write the equation in standard form for the hyperbola 9y2−x2=369y^2 - x^2 = 36.\newline______
  1. Identify Operation: Identify the operation to write the equation in standard form.\newlineDivide both sides by 3636 to isolate the terms involving xx and yy on one side and the constant on the other side.\newlineOperation: Division
  2. Perform Division: Perform the division operation on the equation 9y2−x2=369y^2 - x^2 = 36. Divide each term by 3636: (9y2)/36−(x2)/36=36/36(9y^2)/36 - (x^2)/36 = 36/36 Simplify each term: y2/4−x2/36=1y^2/4 - x^2/36 = 1
  3. Rewrite Equation: Rewrite the equation to match the standard form of a hyperbola.\newlineThe standard form of a hyperbola is (y2a2)−(x2b2)=1(\frac{y^2}{a^2}) - (\frac{x^2}{b^2}) = 1, where aa and bb are constants.\newlineIn this case, a2=4a^2 = 4 and b2=36b^2 = 36, so a=2a = 2 and b=6b = 6.\newlineThe standard form of the hyperbola is:\newliney24−x236=1\frac{y^2}{4} - \frac{x^2}{36} = 1

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