Identify Critical Points

Key Questions

  • What do h and k represent with respect to a hyperbola?

    (h,k)->(x,y) represents the center of the hyperbola, ellipse, and circle.

    (h,k)->(x,y) represents the vertex of the parabola.

    AJ Speller · · Sep 28 2014
  • How do I determine the asymptotes of a hyperbola?

    If a hyperbola has an equation of the form {x^2}/{a^2}-{y^2}/{b^2}=1 (a>0, b>0), then its slant asymptotes are y=pm b/ax.

    Let us look at some details.

    By observing,

    {x^2}/{a^2}-{y^2}/{b^2}=1

    by subtracting {x^2}/{a^2},

    Rightarrow -{y^2}/{b^2}=-{x^2}/{a^2}+1

    by multiplying by -b^2,

    Rightarrow y^2={b^2}/{a^2}x^2-b^2

    by taking the square-root,

    Rightarrow y=pm sqrt{ {b^2}/{a^2}x^2-b^2 } approx pm sqrt{{b^2}/{a^2}x^2}=pm b/a x

    (Note that when x is large, -b^2 is negligible.)

    Hence, its slant asymptotes are y=pm b/a x.

    Wataru · · Sep 28 2014
  • What are the critical points of a hyperbola?

    Critical points are points on the graph of a function where the first order derivative changes signs or equals to zero.

    (Iam assuming you mean or you want something else )

    Konstantinos Michailidis · 1 · Sep 20 2015
  • How do I determine whether a hyperbola opens horizontally or vertically?

    Make the equation be in the form

    (x - h)^2/a^2 - (y - k)^2/b^2 = 1

    or

    (y - k)^2/a^2 - (x - h)^2/b^2 = 1

    If x is on front, the hyperbola opens horizontally
    If y is on front, the hyperbola opens vertically

    seph · 5 · Oct 12 2014

Questions

Geometry of a Hyperbola