MHB How to Determine the Reflection of a Parabola by a Given Line?

[Monoxdifly]

Determine the reflection of a parabola $$y^2-2y-4x-11=0$$ by the line y = -x.

I know how to do it graphically, but please tell me how to do it algebraically.

 

[castor28]

Determine the reflection of a parabola $$y^2-2y-4x-11=0$$ by the line y = -x.

I know how to do it graphically, but please tell me how to do it algebraically.

In such a reflection, the images of the points (1,0) and (0,1) are (0, -1) and (-1,0), respectively.

This means that the image of (x,y) is (-y, -x). You only need to substitute that in the equation.

 

[Monoxdifly]

$$(-x)^2-2(-x)-4(-y)-11=0$$?

 

[castor28]

$$(-x)^2-2(-x)-4(-y)-11=0$$?

Yes

 

[skeeter]

[DESMOS=-20,20,-13.35559265442404,13.35559265442404]y^2-2y-4x-11=0;x^2+2x+4y-11=0;y=-x;[/DESMOS]