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Write the equation in standard form for the hyperbola x2−4y2=100x^2 - 4y^2 = 100.\newline______

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Q. Write the equation in standard form for the hyperbola x2−4y2=100x^2 - 4y^2 = 100.\newline______
  1. Identify Operation: Identify the operation to write the equation in standard form.\newlineDivide both sides by 100100 to isolate the terms on the left side.\newlineOperation: Division
  2. Perform Division: Perform the division operation on the equation.\newlinex2−4y2=100x^2 - 4y^2 = 100\newlinex2100−4y2100=100100\frac{x^2}{100} - \frac{4y^2}{100} = \frac{100}{100}\newlinex2100−y225=1\frac{x^2}{100} - \frac{y^2}{25} = 1
  3. Check Standard Form: Check the equation to ensure it is in the standard form of a hyperbola.\newlineThe standard form of a hyperbola is (x2a2)−(y2b2)=1(\frac{x^2}{a^2}) - (\frac{y^2}{b^2}) = 1, where a2a^2 and b2b^2 are the squares of the lengths of the semi-major and semi-minor axes, respectively.\newlineThe equation x2100−y225=1\frac{x^2}{100} - \frac{y^2}{25} = 1 matches this form with a2=100a^2 = 100 and b2=25b^2 = 25.

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