If the points (au^2, 2au) and (av^2, 2av) are | vedclass

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Question

(B) The equation of the line passing through the points $(au^2, 2au)$ and $(av^2, 2av)$ is given by:$y - 2au = \frac{2av - 2au}{av^2 - au^2}(x - au^2)

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$uv + 1 = 0$

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(B) The equation of the line passing through the points $(au^2, 2au)$ and $(av^2, 2av)$ is given by:$y - 2au = \frac{2av - 2au}{av^2 - au^2}(x - au^2)$$y - 2au = \frac{2a(v - u)}{a(v - u)(v + u)}(x - au^2)$$y - 2au = \frac{2}{v + u}(x - au^2)$Since this is a focal chord,it must pass through the focus $(a, 0)$.Substituting $(a, 0)$ into the equation:$0 - 2au = \frac{2}{v + u}(a - au^2)$$-2au = \frac{2a(1 - u^2)}{v + u}$$-u(v + u) = 1 - u^2$$-uv - u^2 = 1 - u^2$$-uv = 1$$uv + 1 = 0$

If the points $(au^2, 2au)$ and $(av^2, 2av)$ are the extremities of a focal chord of the parabola $y^2 = 4ax$,then

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