A rectangular hyperbola has asymptotes at right angles. Its eccentricity is the square root of 2. It is usually drawn as shown here, with the coordinate axes as the asymptotes. Use the slider to vary the values of c and investigate the effect on the hyperbola. The parametric coordinates of the point P are given in the bottom left corner. Move the point P using the slider to change the value of the parameter t. Look at the value of the ratio PS/PM as the point P varies.