If a double ordinate of the parabola y² = 4ax is a length 8a, then the angle between the lines joining the vertex of the parabola to the ends of this double ordinate is __________.

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Solution

Let us suppose that the ends of double ordinate are P(at², 2at) and Q = (at² , −2at)
Given distance PQ = 8a
i.e. 4at = 8a
i.e. t = 2
∴ P is given by (4a, 4a) and Q is given by (4a , −4a)

$Slope of O P = m_{1} = \frac{4 a - 0}{4 a - 0} = 1 and Slope of O Q = m_{2} = \frac{4 a - 0}{- 4 a - 0} = 1 ∴ Angle between O P and O Q is \tan^{- 1} (\frac{m_{1} - m_{2}}{1 + m_{1} - m_{2}}) = \tan^{- 1} (\frac{2}{0}) = \frac{π}{2}$

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If a double ordinate of the parabola y2 = 4ax is a length 8a, then the angle between the lines joining the vertex of the parabola to the ends of this double ordinate is __________.

If a double ordinate of the parabola y² = 4ax is a length 8a, then the angle between the lines joining the vertex of the parabola to the ends of this double ordinate is __________.