"Let the normal at the point on the parabola y2 = 6x pass through the point (5, $-$8). If the tangent at P to the parabola intersects its directrix at the point Q, then the ordinate of the point Q is :"

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Accepted Answer

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Let P(at², 2at) where a = ${3 \over 2}$

T : yt = x + at² So point Q is $\left( { - a,\,at - {a \over t}} \right)$

N : y = $-$tx + 2at + at³ passes through (5, $-$8)

$-$8 = $-$5t + 3t + ${3 \over 2}$t³

$\Rightarrow$ 3t³ $-$ 4t + 16 = 0

$\Rightarrow$ (t + 2) (3t² $-$ 6t + 8) = 0

$\Rightarrow$ t = 2

So ordinate of point Q is $-$${9 \over 4}$.

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Let the normal at the point on the parabola y² = 6x pass through the point (5, $-$8). If the tangent at P to the parabola intersects its directrix at the point Q, then the ordinate of the point Q is :

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Let the normal at the point on the parabola y2 = 6x pass through the point (5, $-$8). If the tangent at P to the parabola intersects its directrix at the point Q, then the ordinate of the point Q is :

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Let the normal at the point on the parabola y² = 6x pass through the point (5, $-$8). If the tangent at P to the parabola intersects its directrix at the point Q, then the ordinate of the point Q is :