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write the length of chord of the parabola y 2 =4ax that passes trough the vertex and inclined to the axis at pi/4

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

Grade:11

1 Answers

Arun
25750 Points
6 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 \sqrt2
 
Regards
Arun (askIITians forum expert)

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