The length of double ordinate of parabola y ^2=8x which subtents an angle 60 degrees at vertex is.
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Double ordinate is a perpendicular line to axis of parabola.
Let's end points of double ordinate of parabola y² = 8x are P ≡ (2t², 4t) and P' ≡(2t², -4t)
Double ordinate subtends an angle 60° at vertex as shown in figure.
So, angle is bisected by axis of parabola.
now, tan30° = 4t/2t² = 2/t
⇒ 1/√3 = 2/t
⇒ t = 2√3
so, end points of double ordinate are P ≡ (24, 8√3) and P' ≡ ( 24 , -8√3)
length of double ordinate = PP' = √{(24 - 24)² + (8√3 + 8√3)²} = 16√3 unit
Hence, length of double ordinate is 16√3 unit
Let's end points of double ordinate of parabola y² = 8x are P ≡ (2t², 4t) and P' ≡(2t², -4t)
Double ordinate subtends an angle 60° at vertex as shown in figure.
So, angle is bisected by axis of parabola.
now, tan30° = 4t/2t² = 2/t
⇒ 1/√3 = 2/t
⇒ t = 2√3
so, end points of double ordinate are P ≡ (24, 8√3) and P' ≡ ( 24 , -8√3)
length of double ordinate = PP' = √{(24 - 24)² + (8√3 + 8√3)²} = 16√3 unit
Hence, length of double ordinate is 16√3 unit
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