Goals and Objectives of the
Hyperbola Module

After completing this module you will be able to: Describe that the equation Ax2 + By2 = P represents a hyperbola when the coefficients A and B have different signs. Write the standard equation of a hyperbola centred at the origin as x2/ a2 - y2/ b2 = 1 or -x2/ a2 + y2/ b2 = 1. Write the standard equation for a hyperbola centred at any point (h, k) as (x - h)2/ a2 - (y - k)2/ b2 = 1 or -(x - h)2/ a2 + (y - k)2/ b2 = 1. Describe that a hyperbola has two axes of symmetry. Describe the axis of symmetry parallel to the x-axis as the horizontal axis of symmetry. Describe the axis of symmetry parallel to the y-axis as the vertical axis of symmetry. Describe what the variables h, k, a and b represent in the standard equation of a hyperbola. Describe the effect that varying h, k, a and b in the standard equation has on the hyperbola. Write the standard equation of a hyperbola using information about its centre coordinates, vertices, asymptote slopes and/or opening directions. Use the standard equation to describe the characteristics of a hyperbola and sketch its graph. Rewrite an equation of a hyperbola from standard form to an equation of the form Ax2 + By2 + Cx + Dy + F = 0. Rewrite an equation of a hyperbola from the general form Ax2 + By2 + Cx + Dy + F = 0 to the standard form. Show that the standard equation of a hyperbola is equal to a general hyperbola equation of the form Ax2 + By2 + Cx + Dy + F = 0. Describe what happens when a plane cuts both nappes of the double-napped cone at various locations and angles.