The lengths of the perpendiculars from the points `(m^(2), 2m), (mn, m+n)` and `(n^(2), 2n)` to the line `x+sqrt3y+3=0` are in

The lengths of the perpendiculars from (m^(2),2m),(mn,m+n) and (n^(2),2n) to the straight line os x cos alpha+y sin a+sin alpha tan alpha=0 are in

Prove that the length of perpendiculars from points P(m^(2),2m)Q(mn,m+n) and R(n^(2),2n) to the line x cos^(2)theta+y sin theta cos theta+sin^(2)theta=0 are in G.P.

Prove that the lengths of the perpendiculars from the points (m^2,2m),(m m^(prime),m+m^(prime)), and (m^(prime2),2m^(prime)) to the line x+y+1=0 are in GP.

Prove that the length of perpendiculars from points 'P(m^2,2m) Q (mn ,m+n) and R(n^2,2n)' to the line x cos^2theta+ysinthetacostheta+sin^2theta=0 are in G.P.

If m and n are length of the perpendicular from origin to the straight lines whose equations are x cot theta - y = 2 cos theta and 4x+3y=-sqrt(5)cos 2theta, (theta in (0, pi)) , respectively, then the value of m^(2)+5n^(2) is

Add: 3m^(2)n + 5mn^(2) - 7mn and 2m^(2)n - mn^(2) + mn

Verify that (m + n) ( m ^(2) - mn + n ^(2)) = m ^(3) + n ^(3)

The coordinates of the point which divides the line segment joining the points (x_(1);y_(1)) and (x_(2);y_(2)) internally in the ratio m:n are given by (x=(mx_(2)+nx_(1))/(m+n);y=(my_(2)+ny_(1))/(m+n))

Simplify the following : (2m + n) (m^(3) - mn + n^(3))