The curve C C\,C has equation
x=2sec23y,x>2,0<y<π6 x = 2\sec^2 3y, \quad x > 2, \quad 0 < y < \frac{\pi}{6} x=2sec23y,x>2,0<y<6πFind dxdy\displaystyle \frac{\text{d}x}{\text{d}y}dydx in terms of yyy.
Hence show that
dydx=pqxx−2 \frac{\text{d}y}{\text{d}x} = \frac{p}{qx\sqrt{x-2}} dxdy=qxx−2pwhere p p\,p is irrational and q q\,q is an integer, stating the values of p p\,p and qqq.
Find the equation of the normal to C C\,C at the point where y=π18\displaystyle y = \frac{\pi}{18}y=18π, giving your answer in the form y=mx+cy = mx + cy=mx+c where m m\,m and c c\,c are exact constants.
