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Suppose I know all the equations related to a parabola defined as $$y^2= 4ax$$. By "all equations", I meant to say the equation of tangent, normal, chord of contact, polar of a point.. everything related to just that form.

So can I just use all those above equations somehow to get all the equations related to a parabola defined as $$x^2 =4by$$ ? $$Or$$

How should I transform all the equations related to a parabola ($y^2=4ax$) to get the equations for the parabola ($x^2=4by$) ?

I have a test and need quick help. So sorry for this stupid question.

Ankit
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1 Answers1

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The first thing you need to do is rotate $\pi/2$ radians: $x= \cos(\pi/2)x'+ \sin(\pi/2)y'= y'$ $y= -\sin(\pi/2)x'+ \cos(\pi/2)y'= -x'$

So $y^2= 4ax$ becomes $(-x')^2= x'^2= 4ay'$

user247327
  • 18,710
  • so do you mean that for all the equations like equation of a tangent or normal I just need to do a rotational shift and replace x and y with x' and y' ? – Ankit Jun 09 '21 at 16:17