I have a parabola that has a focus at $F(0,f),f>0 $ with vertex at $V(0,0).$ If there is a point on the parabola with parametrization $ P(x(t),y(t))$ where $t$ is the parameter, how far is $P$ from $F$ and how far is $P$ from the directrix in terms of $t$ ?
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These may help http://mathworld.wolfram.com/Parabola.html https://en.wikipedia.org/wiki/Parabola – Shuri2060 Jul 18 '17 at 20:53
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In general if the eqation of parabola is y^2=4ax, the distance of any point (x1,y1) from directrix is( x1+a) In your case eqation of the parabola is x^2=4ty as focus is (0,t) Thus distance of (x,y) from the directrix is (t+y)
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1Can you please improve this answer by formatting it using MathJax? – Xander Henderson Jun 26 '18 at 19:40