A double ordinate of the curve y2 = 4ax is of length 8a prove that the

1.	A double ordinate of the curve y2 = 4ax is of length 8a prove that the lines from the vertex to its ends are at right angles.
Answer» Let P = (at², 2at) and P' = (at², –2at) be the ends of double cordinate PP'. Then 8a = PP' = √(0 + (4at)²) = 4at ⇒ t = 2. ∴ P = (4a, 4a), P' = (4a, –4a) Slope of bar(AP) × slope of bar(AP') (4a/4a)(- 4a/4a) = –1 ∴ ∠PAP' = π/2.

A double ordinate of the curve y2 = 4ax is of length 8a prove that the lines from the vertex to its ends are at right angles.

Answer»

Let P = (at², 2at) and P' = (at², –2at) be the ends of double cordinate PP'.

Then

8a = PP' = √(0 + (4at)²) = 4at ⇒ t = 2.

∴ P = (4a, 4a), P' = (4a, –4a)

Slope of bar(AP) × slope of bar(AP')

(4a/4a)(- 4a/4a) = –1

∴ ∠PAP' = π/2.

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A double ordinate of the curve y2 = 4ax is of length 8a prove that the lines from the vertex to its ends are at right angles.

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