Question

In a parabola y²=4ax, the length of the
chord passing through the vertex & inclined to
the x-axis @ an angle π/6 (pi/6) is?


Step plz

Answer 1

what's the trouble?

The vertex is at (0,0), and tan(π/6) = 1/√3 so the line of the chord is y=x/√3

Now, see where the chord intersects the parabola:
(x/√3)^2 = 4ax
x^2/3 = 4ax
x = 12a

So, the length of the chord is

√((12a)^2 + 64a^2) = 4a√13