Q. Write the equation in standard form for the hyperbola x2−4y2=100.______
Identify Operation: Identify the operation to write the equation in standard form.Divide both sides by 100 to isolate the terms on the left side.Operation: Division
Perform Division: Perform the division operation on the equation.x2−4y2=100100x2−1004y2=100100100x2−25y2=1
Check Standard Form: Check the equation to ensure it is in the standard form of a hyperbola.The standard form of a hyperbola is (a2x2)−(b2y2)=1, where a2 and b2 are the squares of the lengths of the semi-major and semi-minor axes, respectively.The equation 100x2−25y2=1 matches this form with a2=100 and b2=25.
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