Parabola Formula


#1

What is the Combined equation of normal to parabola at the focii? For EXAMPLE in the following sum

y^2 = 4ax
end point of L.R.
 L (a, 2a) , L’ (a,– 2a)
 t1 = 1, t2 = – 1
eqn of normals are
y + t x = 2at + at3
y + x = 3a
y – x = – 3a
combined equation of normal’s are
NOW THIS MY DOUBT WHY WOULD WE GET SUCH A STEP
[y + (x – 3a)] [y – (x – 3a)] = 0
-----> THIS [Eq1*Eq2=0] ???


#2

I am unable to understand the context of the doubt. You have asked why the step exists. Which means you are referring to a solution that you have already seen somewhere. Right? Can you pls show the screenshot of that solution so that I can help out.

I think the simplest answer would be this though.

These two equations have already been given and understood

y+x = 3a --> y+ (x-3a) = 0
y-x = -3a --> y- (x-3a) = 0

Multiplying both sides of the given equations lets you arrive at the step in question.

Does this help? If not, pls show the solution you are referring to so that we can proceed.