Paragraph: Read the following write up carefully and answer the following questions: If (x₁, y₁ ) is the image (reflection) of the point (x, y) in the line y=m x , then x ₁= 1- m ^2 1+ m ^2 x + 2 ~m 1+ m ^2 y and y ₁= 2 ~m 1+ m ^2 x + m ^2-1 1+ m ^2 y [ array l x₁ y₁ array ]= [ array cc 1-m^2 1+m^2 & 2 m 1+m^2 2 m 1+m^2 & m^2-1 1+m^2 array ] [ array l x y array ] X₁=A X X=A⁻¹ X₁ [ array l x y array ]= [ array cc 1-m^

Step-by-step solution

Any point on the parabola is (t^2, t ) . Shift the origin to (-4,0) so that the line becomes X+y=0 and the point (t^2 . , .t ) becomes (4+t^2, t ) where X=x+4 . If (X₁, y₁ ) is the image of (4+t^2, t ) in x+y=0 , then [ array l X₁ y₁ array ]= [ array cc 0 & -1 -1 & 0 array ] [ array c 4+t^2 t array ] x₁=-t, y₁=- (4+t^2 ) and in the original coordinates x₁=-4-t, y₁=-4-t^2 the equation of image is (x+4)^2=-(y+4) .