Show that product of the perpendicular distances from origin to pair of lines represented by `ax^(2)+2hxy+by^(2)+2gx+2fy+c=0` is `(|c|)/(sqrt((a-b)^(2)+4h^(2)))`

IF the pair of lines represented by ax^(2)+2hxy+by^(2)+2gx+2fy+c=0 intersect on the y-axis, then show that 2fgh-bg^(2)-ch^(2)=0

If theta is the angle between the pair of lines represented by ax^2 + 2hxy + by^2 = 0 , then prove that cos theta= (|a+b|)/(sqrt((a-b)^2 + 4h^2))

Show that the product of the perpendicular from (alpha,beta) to the pair of lines S-= ax^(2)+2hxy+by^(2)+2gx+2fy+c=0 is (|aalpha^(2)+2halphabeta+2galpha+2fbeta+c|)/(sqrt((a-b)^(2)+4h^(2))) Hence or otherwise find the product of the perpendicular from the origin

Show that the product of perpendicular from (alpha, beta) to the pair of lines ax^2 + 2hxy + by^2= 0 is |(aalpha^2 + 2h alpha beta + b beta^2)/(sqrt((a-b)^2 - (2h)^2))|

If ax ^(2) + 2kxy + by ^(2) + 2gx + 2fy + c =0 then (dy)/(dx) =

If the slope of one of the lines represented by ax^(2) + 2hxy + by^(2) = 0 is the square of the other, then (a+b)/h+(8h^(2))/(ab)