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Study Guides > College Algebra

Key Concepts & Glossary

Key Equations

Hyperbola, center at origin, transverse axis on x-axis x2a2y2b2=1\frac{{x}^{2}}{{a}^{2}}-\frac{{y}^{2}}{{b}^{2}}=1
Hyperbola, center at origin, transverse axis on y-axis y2a2x2b2=1\frac{{y}^{2}}{{a}^{2}}-\frac{{x}^{2}}{{b}^{2}}=1
Hyperbola, center at (h,k)\left(h,k\right), transverse axis parallel to x-axis (xh)2a2(yk)2b2=1\frac{{\left(x-h\right)}^{2}}{{a}^{2}}-\frac{{\left(y-k\right)}^{2}}{{b}^{2}}=1
Hyperbola, center at (h,k)\left(h,k\right), transverse axis parallel to y-axis (yk)2a2(xh)2b2=1\frac{{\left(y-k\right)}^{2}}{{a}^{2}}-\frac{{\left(x-h\right)}^{2}}{{b}^{2}}=1

Key Concepts

  • A hyperbola is the set of all points (x,y)\left(x,y\right) in a plane such that the difference of the distances between (x,y)\left(x,y\right) and the foci is a positive constant.
  • The standard form of a hyperbola can be used to locate its vertices and foci.
  • When given the coordinates of the foci and vertices of a hyperbola, we can write the equation of the hyperbola in standard form.
  • When given an equation for a hyperbola, we can identify its vertices, co-vertices, foci, asymptotes, and lengths and positions of the transverse and conjugate axes in order to graph the hyperbola.
  • Real-world situations can be modeled using the standard equations of hyperbolas. For instance, given the dimensions of a natural draft cooling tower, we can find a hyperbolic equation that models its sides.

Glossary

center of a hyperbola
the midpoint of both the transverse and conjugate axes of a hyperbola
conjugate axis
the axis of a hyperbola that is perpendicular to the transverse axis and has the co-vertices as its endpoints
hyperbola
the set of all points (x,y)\left(x,y\right) in a plane such that the difference of the distances between (x,y)\left(x,y\right) and the foci is a positive constant
transverse axis
the axis of a hyperbola that includes the foci and has the vertices as its endpoints

Licenses & Attributions