Multiple choice general knowledge math & puzzles

x² /a² - y²/b² = 1 is the equation of a hyperbola. When |x| is very high the graph for the above equation resembles –

  1. cycloid

  2. parabola

  3. ellipse

  4. straight line
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For the hyperbola x²/a² - y²/b² = 1, as |x| approaches infinity, the curve approaches its asymptotes y = ±(b/a)x, which are straight lines passing through the origin. This asymptotic behavior is fundamental to hyperbola geometry.

AI explanation

A hyperbola x^2/a^2 - y^2/b^2 = 1 has two straight-line asymptotes, y = ±(b/a)x, that the curve gets closer and closer to as |x| grows large. So for very large |x|, the hyperbola's branches hug these straight lines rather than curving like a parabola or closing up like an ellipse.

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