Question

What is length of the chord of the parabola y²=4ax, which passes through the vertex and is inclined to the axis at π/4.

Answer 1

Let AB be the chord with vertex A( 0,0) Given α = 45°

equation of of AB = ( y - 0) = tan 45( x - 0)

y = x then y = 4a ⇒ x = 4a

∴ B = ( 4a , 4a)
Length of chord AB = 4√2a.