Show that the sum of the squares of the perpendiculars from the origin upon the lines `xcosalpha+ysinalpha=acos2alphaandxsecalpha+ycossecalpha=2a` is independent of `alpha`.

Find the foot of the perpendicular from the point (2,4) upon x+y=1.

The co-ordinates of the foot of the perpendicular from (0, 0) upon the line x+y=2 are

Using calculus find the length of the perpendicular from the point (2,-1) upon the line 3x-4y+5 =0.

Find the locus of the foot of the perpendicular from the origin upon a stright line which always passes through the point (2,3).

find the length of the perpendicular drawn from the point (2,1,-1) on the line x - 2y + 4z = 9

If p and q are the lengths of the perpendiculars from the origin to the straight lines x "sec" alpha + y " cosec" alpha = a " and " x "cos" alpha-y " sin" alpha = a "cos" 2alpha, " then prove that 4p^(2) + q^(2) = a^(2).

Find the perpendicular distance from the origin of the straight line 3x+4y=5sqrt(2) ,

If p and q are the lengths of perpendiculars from the origin to the lines xcostheta-ysintheta=kcos2theta and xsec""theta+y" cosec"""theta=""k , respectively, prove that p^2+4q^2=k^2 .

Show that the four straight lines xcosalpha+ysinalpha=P , xsinalpha-ycosalpha=-p and xsinalpha-ycosalpha=P form a square.

Show that the product of the perpendiculars from the two points (+-4,0) upon the straight linee 3xcostheta+5ysintheta=15 is independent of theta .