Question
Download Solution PDFIn the parabola y2 = x, what is the length of the chord passing through the vertex and inclined to the x-axis at an angle θ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
The coordinates of the point where the chord cut the parabola satisfIes the equation of a parabola.
Calculation:
Given:
The equation of a parabola is y2 = x.
The angle made by Chord OA with x-axis is θ
Let the length of the chord OA of the parabola is L
So, Length of AM = L sinθ
and Length of OM = L cosθ
So, The coordinate of A = (L cos θ, L sin θ)
And this point will satisfy the equation of parabola y2 = x.
⇒ (Lsin θ)2 = L cos θ
⇒L2 sin2 θ = L cos θ
⇒ L = cos θ. cosec2 θ
∴ The required length of chord is cos θ. cosec2 θ.
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