1. A curve has equation y = x(x-a)(x+a), where a is a constant. Find the equations of the tangents to the graph at the points where is crosses the x-axis.

There are 3 equations in total, but I cant seem to get the 3rd equation.
This is how I get the first 2 equations:

y = x³-a²x
dy/dx = 3x²-a²

(x-intercept, y=0)
x³-a²x = 0
x² = a²
x = a, -x = -a

3x²-a² = 3a²-a² = 2a²

Therefore, equations of tangents:
y = 2a²x-2a³, y = 2a²x+2a³

The third equation: y = -a²x
I wonder how to get the third equation?


2. Find the coordinates of the point of intersection of the tangents to the graph of y = x² at the points at which it meets the line with equation y = x+2

As for this question, I have completely no idea on what to do...the answer is (1/2,-2)