Hyperbolas Practice

Hyperbola - the set of all points in a plane, the DIFFERENCE of whose distances from two distinct fixed points, the foci, is a positive constant. Hyperbolas are formed by slicing a double-napped cone PERPENDICULAR to the base. Branch Conjugate Z - - - -- Vertex Center Transverse axis Branch ; Vertex (h + a, k) Standard Equation of a Hyperbola (x-h)2 (-k)2 _(x-h) = 1 (Horizontal Transverse Axis) (Vertical Transverse Axis) Problem Graph the following hyperbolas: 36 () _ 2 = 1 (x-1)2 _()+2) = 1 16 (-3)2 _(2) = 1 How to Locate Foci Foci are located "c" units from the center on the TRANSVERSE axis Foci can be calculated using the following formula: c2 = a2 + b2 or c = Vaz + bz Problem 2 Find the standard form of the equation of the hyperbola with foci (-1,2) and (-1,-8) and vertices (-1,1) and (-1,-7) Asymptotes of a Hyperbola y= k -(x - h) Asymptotes for horizontal transverse axis y = kt"(x - h) Problem 3 What are the equations of the asymptotes for the following hyperbola? -x2 + 5y2 = 125 Problem 4 Sketch the hyperbola given by -16x2 + y2 + 32x + 4y - 76 = 0, and find the equations of the asymptotes