Q. 9 Find the equations of the chords of the parabola y2 = 4ax which pass through the point (-6a, 0) and which subtends an angle of 45° at the vertex.

The vertex of parabola 𝑦2=4𝑎𝑥
is (0,0).
Equation of a chord in the slope-intercept form is
y=kx+b (1)
Here k=tan 45°=1, because a chord subtends an angle of 45° at the vertex.
So, in fact (1) is given by
y=x+b (2)
On the other hand, this line passes through the point (–6a, 0), consequently its coordinates satisfy equation (2):
0=-6a+b,
b=6a.
Finally, y=x+6a is the equation of chord.
Answer: y=x+6a.