Prove that the product of the perpendiculars from `(alpha,beta)` to the pair of lines `a x^2+2h x y+b y^2=0` is `(aalpha^2+2halphabeta+b beta^2)/(sqrt((a-b)^2+4h^2))`

The product of the perpendiculars from (-1,2) to the pair of lines 2x^(2)5xy+2y^(2)=0

The product of the perpendiculars drawn from the point (1,2) to the pair of lines x^(2)+4xy+y^(2)=0 is

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

The point of intersection of the pair of lines x^(2)+xy+2y^(2)-3x+2y+4=0 is (alpha,beta) then 2 alpha+beta=

Prove that the product of the lengths of the perpendiculars drawn from the points (sqrt(a^2-b^2),""""0) and (-sqrt(a^2-b^2),""""0) to the line x/a costheta + y/b sintheta=1 is b^2 .

Prove that the equation of the chord joining the points 'a'&'b' on the ellipse x^2/a^2+y^2/b^2=1 is x/a cos((alpha+beta)/2)+y/b sin((alpha+beta)/2)=cos((alpha-beta)/2)