Question #225810

Write down the parametric coordinates of any point on each of the following parabolas.

(a) y2 = 8x

b) y2 = 24x

c) y2 = -16x

d) x2 = 6y


1
Expert's answer
2021-08-15T17:49:48-0400

(a) The parametric coordinates of any point on parabola y2=8xy^2 = 8x :



\begin{cases} x = \dfrac {t^2} 8 \\ y = t \end{cases} \




<t<-\infin < t < \infin



(b) The parametric coordinates of any point on parabola y2=24xy^2 = 24x:



\begin{cases} x = \dfrac {t^2} {24} \\ y = t \end{cases} \




<t<-\infin < t < \infin



(c) The parametric coordinates of any point on parabola y2=16xy^2 = - 16 x :



\begin{cases} x = -\dfrac {t^2} {16} \\ y = t \end{cases} \




<t<-\infin < t < \infin



(d) The parametric coordinates of any point on parabola x2=6yx^2 = 6y :



\begin{cases} x = t \\ y = \dfrac {t^2} 6 \end{cases} \




<t<-\infin < t < \infin

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