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# write the length of chord of the parabola y2=4ax that passes trough the vertex and inclined to the axis at pi/4

Arun
25763 Points
3 years ago
Dear student

Vertex = (0,0)
Now line will be
y -0 = m(x-0)
but m = tan (pi/4) = 1
Hence
Line:
y = x
Now
Its intersection point with parabola
y2 = 4ay
y = 0 then x = 0
And
y = 4a then x = 4a

Now
Intersection point = (4a, 4a)
Hence
Length of chord = length between (0,0) and (4a, 4a)
= 4a $\sqrt$2

Regards