Identify which of the following equations is NOT equivalent to $36x^2 = y^2 - 9$ .

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36x^2 + 9 = y^2

108x^2 = 3y^2 - 27

36x^2 = (y + 3)(y - 3)

6x = y - 3

Correct

x^2 = (y^2 - 9)/36

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Official Explanation

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Let's analyze the equation given: 36x^2 = y^2 - 9, which can be rearranged to y^2 - 36x^2 = 9. This can also be expressed as (y - 3)(y + 3) = 36x^2. Now, let's evaluate the options: A) 36x^2 + 9 = y^2 can be rearranged to 36x^2 = y^2 - 9, which matches the original equation, so this option is eliminated. B) 108x^2 = 3y^2 - 27 can be simplified by dividing by 3, yielding 36x^2 = y^2 - 9, which is equivalent to the original equation, so…

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What this question tests

What it tests

Your ability to manipulate linear and quadratic expressions, substitute unknowns, and solve equations under time pressure.

Common trap

Losing a sign when moving terms across the equals sign, or dividing both sides by a variable that could equal zero.

Identify which of the following equations is NOT equivalent to 36x2=y2−936x^2 = y^2 - 936x2=y2−9.