If the foot of the perpendicular from `(-4,5)` to the straight line `3x-4y-18=0` is `(alpha,beta)` then value of `(alpha+beta)=`

Let PQ be a diameter of the circle x^(2) + y^(2)=9 If alpha and beta are the lengths of the perpendiculars from P and Q on the straight line, x+y=2 respectively, then the maximum value of alpha beta is ______.

Coordinates of the foot of the perpendicular drawn from 0,0 to he line jolning (a cos alpha,a sin alpha) and (a cos beta,a sin beta) are

The foot of perpendicular from (1,2,6) to line (x-3)/(2)=(y+1)/(2)=(z-1)/(-1) is the point (alpha,beta,gamma) then (alpha+beta+gamma)=

If 2x+3y+4=0 is perpendicular bisector of the segment joining the points A(1,2) and B(alpha,beta) then the value of alpha+beta is

PQ is a diameter of circle x^2+y^2=4 . If perpendicular distances of P and Q from line x+y=2 are alpha and beta respectively then maximum value of alpha beta is

If (alpha,beta) is the centre of the circle which touches the curve x^(2)+xy-y^(2)=4 at (2,2) and the line 3x-y+6=0 ,then the value of alpha+beta is equal to

Consider the equation 3x^2 +4x - 5 = 0 , if alpha,beta are the roots, then 1/alpha + 1/beta =

If alpha and beta are the roots of the equation x^(2)-4x+1=0(alpha>beta) then find the value of f(alpha,beta)=(beta^(3))/(2)csc^(2)((1)/(2)tan^(-1)((beta)/(alpha))+(alpha^(3))/(2)sec^(2)((1)/(2)tan^(-1)((alpha)/(beta)))