Let a R.

1. What is the equation of the tangent line L_t to y = x² at x = a?

From now on, assume that a 6= 0.

2. Let L_r be the line obtained by reflecting vertical line x = a about the line L_t. (This models the way in which a ray of light travelling along the line x = a is reflected by a parabolic mirror along y = x² .) Show that the slope of L_r is 4a4a21.

3. Where does the line Lr intersect the y-axis? The correct answer does not depend on a!