Number of normals drawn from $(-2,2)$ to parabola $y^2-2y-2-1=0$ is?
The answer given is 1. I don't understand how a parabola can be represented by this equation. Is there a way of bringing this to a standard form such as $y^2=4ax$ or $x^2=4ay$? The solution given says these two things: the equation $$ (y-1) = m(x+1) - 2am -m^3 $$ and that $a = 1/2$. I know that $ y = mx - 2am -m^3 $ is the standard equation for a normal to a parabola, but how did they get this one? Also, how is $a=1/2$?