Let `S^1 = 0` be the image or reflection of the curve `S=0` about the line mirror `L=0`. Suppose P be any point on the curve `S=0` and Q be the image about the line mirror L=0, then Q will lie on `S^1=0` . Let the given curve be `S : f(x, y)` line mirror L : ax + by + c = 0 . We take a 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 = 0 and parameter. Let `Q(phi(t), psi(t))` where t is a parameter. Now let `x=phi(t)` and `y=psi(t)` Eliminating t, we get the equation of the reflected curve `S^1` .Then answer the following questions. The image of the parabola `x^2=4y` in the line x+y=a is

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 parabola x^(2) = 4y in the line x+y=a is

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

The image of the point A (1,2) by the line mirror y=x is the point B and the image of B by the line mirror y=0 is the point (alpha,beta) , then

The combined equation of the images of pair of lines given by ax^2+2hxy+by^2=0 in the line mirror y=0 , is

The mirror image of any point on the directrix of the parabola y^(2)=4(x+1) in the line mirror x+2y=3-0 lies on 3x-4y+4k=0, Then k=

The image of the pair of lines represented by ax^(2)+2hxy+by^(2)=0 by the line mirror y=0 is

The image of the pair of lines represented by ax^(2)+2hxy+by^(2)=0 by the line mirror y=0 is