What is the least value of $z$ such that 3 normals from $P(z,0)$ can be drawn to $y^2=4ax$?
I thought that any point inside the parabola should satisfy this condition but I was proven wrong.
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Parcly Taxel
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palash jain
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See https://math.stackexchange.com/questions/475698/condition-on-a-point-on-axis-of-the-parabola-so-that-3-distinct-normals-can-be and https://math.stackexchange.com/questions/1601215/finding-the-number-of-normals-to-a-parabola – lab bhattacharjee May 05 '17 at 16:39
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Ty very much 4 this link #lab bhattacharjee – palash jain May 05 '17 at 16:48
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Hint...write down the equation of the normal at $(at^2,2at)$ and plug in $x=z,y=0$
The resulting equation in $t$ must have three distinct roots (one of which is zero).
David Quinn
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