[" 8.Show that the product of the perpendiculars from the two "],[" points "(+-4,0)" upon the straight line "3x cos theta+5y sin theta=15" is "],[" independent of "theta" ."]

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

The product of the perpendiculars drawn from the points pm sqrt(a^(2) -b^(2),0) on the line x/a cos theta+ y/b sin theta =1, is

The product of y the perpendiculars from the two points (pm 4, 0) to the line 3x cos phi +5y sin phi =15 is

If p and p_1 be the lengths of the perpendiculars drawn from the origin upon the straight lines x sin theta + y cos theta = 1/2 a sin 2 theta and x cos theta - y sin theta = a cos 2 theta , prove that 4p^2 + p^2_1 = a^2 .

Prove that the product of the length of the perpendiculars from the points (sqrt(a^2 -b^2) , 0) and (-sqrt(a^2 -b^2), 0) to the line x/a cos theta + y/a cos theta + y/b sin theta = 1 is

Foot of the perpendicular from origin to the line joining the points (a cos theta,a sin theta),(a cos phi,a sin phi) is

If p and q are the perpendicular distances from the origin to the straight lines x sec theta - y cosec theta = a and x cos theta + y sin theta = a cos 2 theta , then