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 ______.

P and Q are any two points on the circle x^(2)+y^(2)=4 such that PQ is a diameter.If alpha and beta are the lengths of perpendiculars from P and Q on x+y=1 then the maximum value of alpha beta is

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)=

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

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

Let L be a line obtained from the intersection of two planes x+2y+z = 6 and y+2z=4 . If point P(alpha,beta,gamma) is the foot of perpendicular from (3,2,1) on L then the value of 21(alpha+beta+gamma) equals .

If the length of the tangent drawn from (alpha,beta) to the circle x^(2)+y^(2)=6 be twice the length of the tangent from the same point to the circle x^(2)+y^(2)+3x+3y=0, then prove that alpha^(2)+beta^(2)+4 alpha+4 beta+2=0

If x^(2)+alpha y^(2)+2 beta y=a^(2) represents a pair of perpendicular lines,then beta=

If alpha and beta are the roots of the equation x^(2)-px +16=0 , such that alpha^(2)+beta^(2)=9 , then the value of p is