Show that the perpendicular distance of the point \((h,k)\) from the straight line \(x\cos\alpha+y\sin\alpha=p\) is the numerical value of \[h\cos\alpha+k\sin\alpha-p.\] [“Numerical value” means ignoring whether it is positive or negative, that is, the absolute value of this expression.]
Calculate the coordinates of the centres of the two circles of radius \(5\) which pass through the point \((4,4)\) and touch the straight line \(3x-4y-28=0\).
