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.
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 $(-x')^2= x'^2= 4ay'$