Find the y-coordinate of all points on the curve $2x + (y+2)^2=0$ where the normal line to the curve passes through the point (-27,-50) (not on curve).
There are 3 answers.
I started by taking the derivative of the function and got: $$dy/dx=mtan=-1/(y+2)$$
So the slope of the normal is $y+2$
I then used the point in the slope=slope formula and got the following equation for the normal line $$xy+26y+2x+4$$ Which I then set equal to the original equation to find the points of intersection, and ended up with $$y^2-xy-22y$$ The general formula for the y values is x + 22, and I don't know how to get 3 values from this.