Suppose the graph of quadratic polynomial `y = x^2 + px + q` is situated so that it has two arcs lying between the rays `y = x and y = 2x, x>=0`. These two arcs are projected onto the x-axis yielding segments `S_L and S_R`, with `S_R` to the right of `S_L`. Find the difference of the length `l(S_R)-l(S_L)`

Find the derivative of (px + q) (r/x + s)

Find the distance between the parallel lines l (x + y) +p = 0 and l (x + y) - r = 0

Find the distance between parallel lines:- l(x+y)+p=0 and l(x+y) -r =0.

Find the distances between parallel lines l(x+y)+p=0 and l(x+y)-r=0

Write the L.H.S and the R.H.S of each of the following equations: (i) x-3=5 (ii) 3x=15-2x

Write the L.H.S and the R.H.S of each of the following equations: x-3=5 (ii) 3x=15-2x

Let l_(1) and l_(2) be the two skew lines. If P, Q are two distinct points on l_(1) and R, S are two distinct points on l_(2) , then prove that PR cannot be parallel to QS.

Let l_(1) and l_(2) be the two skew lines. If P, Q are two distinct points on l_(1) and R, S are two distinct points on l_(2) , then prove that PR cannot be parallel to QS.

Consider the lines L_1 and L_2 defined by L_1:xsqrt2+y-1=0 and L_2:xsqrt2-y+1=0 For a fixed constant lambda , let C be the locus of a point P such that the product of the distance of P from L_1 and the distance of P from L_2 is lambda^2 . The line y=2x+1 meets C at two points R and S, where the distance between R and S is sqrt(270) . Let the perpendicular bisector of RS meet C at two distinct points R' and S' . Let D be the square of the distance between R' and S'. The value of lambda^2 is