There are 4 types of standard parabolas , and I'm supposed to remember many formulas about them like tangent , normal etc.

But the problem is , if i know a certain formula for $y^2=4ax $ how can i convert it so that it is applicable to $x^2=4ay$?

It doesn't look as simple as exchanging x and y.


For these, simply exchange $x$ and $y$ for converting the applicability of formulas from $y^2=4ax$ to $x^2=4ay$:

(The given formulas are for the parabola $y^2=4ax$)

  1. Equation of directrix. ($x=-a$)
  2. Equation of the axis. ($y=0$)
  3. Focal distance of a point P($x,y$). ($x+a$)
  4. Parametric equations. ($x=at^2,\;y=2at$)
  5. Parametric equation of tangent. ($ty=x+at^2$)
  6. Parametric equation of normal. ($y+tx=2at+at^3$)

If you want to convert the applicability of above formulas from $y^2=4ax$ to $y^2=-4ax$, put $x=-x$ in the original formula.


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