Show that the reflection of the line `px+qy+r=0` in the line `x+y+1 =0` is the line `qx+py+(p+q-r)=0,` where `p!= -q`.

Show that the reflection of the line a x+b y+c=0 on the line x+y+1=0 is the line b+a y+(a+b-c)=0 where a!=bdot

Show that the reflection of the line a x+b y+c=0 on the line x+y+1=0 is the line bx+a y+(a+b-c)=0 where a!=bdot

Find the reflection of the point Q(2,1) in the line y + 3 = 0

The point of injtersection of the line x/p+y/q=1 and x/q+y/p=1 lies on the line

Show that the roots of the equation x^3 +px^2 +qx +r=0 are in A.P 2p^3 - 9 pq + 27 r=0

Show that the roots of the equation x^3 +px^2 +qx +r=0 are in H.P then 2q^3 =9r (pq-3r)

If the line y+2x+3=0 is parallel to the line 2y-px-4=0 , what is the value of p ?

show that the condition that the roots of x^3 + px^2 + qx +r=0 may be in G.P is p^3 r=q^3

show that the condition that the roots of x^3 + 3 px^2 + 3 qx +r=0 may be in h.P is 2q^3=r (3 pq -r)

Let S' be the image or reflection of the curve S = 0 about line mirror L = 0 Suppose P be any point on the curve S = 0 and Q be the image or reflection about the line mirror L = 0 then Q will lie on S' = 0 How to find the image or reflection of a curve ? Let the given be S : f( x,y) = 0 and the line mirror L : ax+by+c = 0 We take point P on the given curve in parametric form . Suppose Q be the image or reflection of point P about line mirror L = 0 which again contains the same parameter L et Q -= (phi (t) , (t)), where t is parameter . Now let x = phi (t) and y = (t) Eliminating t , we get the equation of the reflected curve S' The image of the circle x^(2)+y^(2) = 4 in the line x+ y = 2 is