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Write the equation in standard form for the hyperbola 4x2−y2=164x^2 - y^2 = 16.\newline______

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Q. Write the equation in standard form for the hyperbola 4x2−y2=164x^2 - y^2 = 16.\newline______
  1. Identify Operation: Identify the operation to write the equation in standard form.\newlineDivide both sides by 1616 to isolate the terms on the left side of the equation.\newlineOperation: Division
  2. Perform Division: Perform the division operation on the equation 4x2−y2=164x^2 - y^2 = 16. Divide each term by 1616: (4x2)/16−(y2)/16=16/16(4x^2)/16 - (y^2)/16 = 16/16 Simplify each term: x2/4−y2/16=1x^2/4 - y^2/16 = 1
  3. Check Standard Form: Check the resulting equation to ensure it is in standard form for a hyperbola.\newlineThe standard form for a hyperbola is (x2a2)−(y2b2)=1(\frac{x^2}{a^2}) - (\frac{y^2}{b^2}) = 1, where aa and bb are real numbers.\newlineThe equation x24−y216=1\frac{x^2}{4} - \frac{y^2}{16} = 1 matches this form, with a2=4a^2 = 4 and b2=16b^2 = 16.

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