The asymptotes are straight lines with opposite gradient representing the limits for x and y as they approach infinity and minus infinity. The hyperbola is in standard form but the origin is offset from (0,0) to the point (-2,2). The asymptotes cross at this point like the centre of an X. The slopes of the asymptotes are found by taking the square roots of the x and y terms: (x+2)/20 and (y-2)/15. When x and, therefore, y are very large we have (x+2)/20=+/-(y-2)/15, so y=2+/-15/20, i.e., 2+/-3/4. Therefore the slopes of the asymptotes are 3/4 and -3/4. The standard form of a linear equation is y=ax+b, where a is the slope, so we can write for each asymptote y=3x/4+b and y=-3x/4+b, where b assumes a different value in each equation. The asymptotes cross at (-2,2) so these values of x and y satisfy both equations. This enables us to find b in each case. 2=3*(-2)/4+b and 2=-3*(-2)/4+b. This gives values 7/2 and 1/2 for b, so the asymptotes are y=3x/4+7/2 and y=1/2-3x/4.