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Q.
The coordinate of the point on the parabola $y^{2}=8 x$ which is at minimum distance from the circle $x ^{2}+( y +6)^{2}=1$ are
Conic Sections
Solution:
Let $P \left(2 t ^{2}, 4 t \right)$ be any point on the parabola, equation of normal at $P \left(2 t ^{2}, 4 t \right)$ $y+t x=4 t+2 t^{3}$
this normal passes through $(0,-6)$
$-6+0=4 t+2 t^{3} $
$t^{3}+2 t+3=0 $
$(t+1)\left(t^{2}-t+3\right)=0 $
$t=-1, t^{2}-t+3=0$
$D < 0$
$P(2,-4) $
