Graphing hyperbolas Sketch the graph of the following hyperbolas. Specify the coordinates of the vertices and foci and find the equations of the asymptotes. Use a graphing utility to check your work.

Solution 43EStep 1:Given :The general equation of hyperbola Comparing the equation with the general equation, we get Using a and b, we find the eccentricity of the hyperbola Step 3:Vertices of the hyperbola are . Using the values of h,a and k, we getFoci of the hyperbola are . Using the values of h,a,e and k, we getEquations of the asymptotes of the hyperbola of form are:Using the values of h,a,b and k, we get.Hence the hyperbola has vertices () , foci and asymptotes .Sketch of the hyperbola is: