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Let the normal at the point P on the parabola $y^{2}=6 x$ 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:
Option: 1
$-3$

Option: 2
$-\frac{9}{4}$

Option: 3
$-\frac{5}{2}$

Option: 4
$-2$

Answers (1)

best_answer

Equation of normal : $\mathrm{y=-tx+2at+at^{3}}$ $\mathrm{\because \left ( a= \frac{3}{2} \right )}$

Since passing through $\mathrm{\left ( 5,-8 \right )}$ , we get $\mathrm{t=-2}$

Co-ordinate of $\mathrm{Q:\left ( 6,-6 \right )}$

Equation of tangent at $\mathrm{Q:x+2y+6=0}$

Put $\mathrm{x=\frac{-3}{2}}$ to get $\mathrm{R=\left ( \frac{-3}{2},\frac{-9}{4} \right )}$

Hence the correct answer is option 2.

Posted by

sudhir.kumar

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