Write the tangent lines to the curve

[Jpyhsics]

Homework Statement

Write the equations of tangent lines to the curve of the implicit function x²+2x+2y²-4y=5
that are normal to the line y=x+122. The attempt at a solution
I know that the slope has to be m=-1
I found the derivative using implicit differentiation:
dy/dx=(-2x-2)/(4y-4)

Now I am unsure how to find the points, please help it is due tomorrow.

 

[FactChecker]

The derivative must equal -1. That should give you an equation that you can solve for y in terms of x. You can replace y in your original function equation and solve it for x.