Find the asymptotes of the hyperbola (x^2 / 9) - (y^2 / 16) = 1.
Answer and explanation
Correct answer: D. y = +-(4/3)x
- Step 1: The standard horizontal hyperbola equation is (x^2 / a^2) - (y^2 / b^2) = 1.
- Step 2: Identify a and b: a^2 = 9 so a = 3; b^2 = 16 so b = 4.
- Step 3: Asymptote equation for horizontal hyperbola: y = +-(b/a)x.
- Step 4: Substitute values: y = +-(4/3)x.
Answer
y = +-(4/3)x.
Why not the others: 'y = +-(3/4)x' inverts the ratio as +-(a/b)x; 'y = +-(16/9)x' uses b^2 / a^2 instead of b / a; 'y = +-(9/16)x' uses a^2 / b^2.
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